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Search: a062672 -id:a062672
Displaying 1-10 of 17 results found. page 1 2
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A062664 Composite and every divisor (except for 1) contains the digit 2. +10
18
254, 422, 482, 502, 526, 529, 542, 562, 842, 1042, 1642, 2042, 2246, 2258, 2402, 2426, 2434, 2446, 2458, 2462, 2474, 2498, 2518, 2554, 2558, 2566, 2578, 2582, 2594, 2642, 2654, 2846, 2854, 2858, 2921, 3242, 3254, 3442, 4022, 4126, 4162, 4222, 4226 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If k is in the sequence, then all composite divisors of k are in the sequence. - Robert Israel, Jul 11 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
254 has divisors 1, 2, 127 and 254, all of which except for 1 contain the digit 2.
MAPLE
filter:= proc(n) local D;
if isprime(n) then return false fi;
andmap(con2, numtheory:-divisors(n) minus {1})
end proc:
con2:= proc(n) option remember; member(2, convert(n, base, 10)) end proc:
select(filter, [$4..10000]); # Robert Israel, Jul 11 2019
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 4230], !PrimeQ[#] && fQ[#, 2] &] (* Robert G. Wilson v, Jun 11 2014 *)
PROG
(Magma) [m:m in [2..4300] | not IsPrime(m) and #[d:d in Divisors(m)|2 in Intseq(d)] eq #Divisors(m)-1]; // Marius A. Burtea, Jul 11 2019
CROSSREFS
Cf. A062649, A062668, A062670, A062672, A062674, A062676, A062678, A062680, A243819.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset changed by Robert Israel, Jul 11 2019
STATUS
approved
A062667 Every divisor (except 1) contains the digit 3. +10
18
3, 13, 23, 31, 37, 39, 43, 53, 73, 83, 93, 103, 113, 131, 137, 139, 163, 173, 193, 223, 233, 239, 263, 283, 293, 307, 309, 311, 313, 317, 331, 337, 339, 347, 349, 353, 359, 367, 373, 379, 383, 389, 393, 397, 403, 431, 433, 439, 443, 463, 503, 523, 563, 593 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
93 has divisors 1, 3, 31 and 93, all of which contain the digit 3.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 600], fQ[#, 3] &] (* Robert G. Wilson v, Jun 11 2014 *)
CROSSREFS
Cf. A062653, A062664, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
STATUS
approved
A062669 Every divisor (except 1) contains the digit 4. +10
18
41, 43, 47, 149, 241, 347, 349, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 541, 547, 641, 643, 647, 743, 941, 947, 1049, 1249, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1849 has divisors 1, 43 and 1849, the last two of which contain the digit 4.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1500], fQ[#, 4] &] (* Robert G. Wilson v, Jun 11 2014 *)
Select[Range[2, 1500], AllTrue[Rest[Divisors[#]], DigitCount[#, 10, 4]>0&]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 05 2021 *)
PROG
(Magma) [k:k in [2..1500]| forall{d:d in Set(Divisors(k)) diff {1}| 4 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
Example corrected by Harvey P. Dale, Jun 05 2021
STATUS
approved
A062670 Composite and every divisor (except 1) contains the digit 4. +10
18
1849, 6407, 14227, 14309, 14921, 16403, 16441, 17243, 18409, 18847, 19049, 19147, 20459, 20941, 21457, 21479, 21949, 22427, 23453, 25427, 27649, 30409, 30463, 31949, 34921, 40463, 40721, 43009, 44227, 44509, 45107, 49303, 58343, 59491 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1849 has divisors 1, 43 and 1849, all of which contain the digit 4.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 59500], !PrimeQ[#] && fQ[#, 4] &] (* Robert G. Wilson v, Jun 11 2014 *)
d4Q[n_]:=CompositeQ[n]&&AllTrue[Rest[Divisors[n]], DigitCount[#, 10, 4]>0&]; Select[Range[ 60000], d4Q] (* Harvey P. Dale, Jun 20 2023 *)
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
STATUS
approved
A062671 Every divisor (except 1) contains the digit 5. +10
18
5, 25, 53, 59, 125, 151, 157, 251, 257, 265, 295, 353, 359, 457, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 625, 653, 659, 751, 755, 757, 785, 853, 857, 859, 953, 1051, 1151, 1153, 1255, 1259, 1285, 1325, 1451, 1453, 1459, 1475, 1511 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
25 has divisors 1, 5 and 25, all of which (except 1) contain the digit 5.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1500], fQ[#, 5] &] (* Robert G. Wilson v, Jun 11 2014 *)
PROG
(Magma) [k:k in [2..1500]| forall{d:d in Set(Divisors(k)) diff {1}| 5 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
(Python)
from sympy import divisors
def ok(n): return all('5' in str(d) for d in divisors(n)[1:])
print(list(filter(ok, range(2, 1512)))) # Michael S. Branicky, May 25 2021
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
STATUS
approved
A062673 Every divisor (except 1) contains the digit 6. +10
18
61, 67, 163, 167, 263, 269, 367, 461, 463, 467, 563, 569, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 761, 769, 863, 967, 1061, 1063, 1069, 1163, 1361, 1367, 1567, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
26569 has divisors 163 and 26569, each of which contains the digit 6.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1660], fQ[#, 6] &] (* Robert G. Wilson v, Jun 11 2014 *)
PROG
(Magma) [k:k in [2..1700]| forall{d:d in Set(Divisors(k)) diff {1}| 6 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062674, A062675, A062676, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
STATUS
approved
A062674 Composite and every divisor (except 1) contains the digit 6. +10
18
16043, 16409, 17621, 26569, 36661, 37637, 39467, 40267, 40669, 41663, 42869, 45761, 46297, 46421, 46909, 52643, 61289, 64721, 64789, 64843, 65209, 69169, 71623, 72361, 75469, 76121, 76987, 91769, 96521, 97661, 97963, 100367, 101369 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
26569 has divisors 163 and 26569, all of which contain the digit 6.
MATHEMATICA
Select[Range[2, 102000], !PrimeQ[#]&&And@@(MemberQ[IntegerDigits[#], 6]&/@ Rest[Divisors[#]])&] (* Harvey P. Dale, May 26 2013 *)
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 101400], !PrimeQ[#] && fQ[#, 6] &] (* Robert G. Wilson v, Jun 11 2014 *)
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062675, A062676, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
STATUS
approved
A062675 Every divisor (except 1) contains the digit 7. +10
18
7, 17, 37, 47, 67, 71, 73, 79, 97, 107, 127, 137, 157, 167, 173, 179, 197, 227, 257, 271, 277, 307, 317, 337, 347, 367, 373, 379, 397, 457, 467, 479, 487, 497, 547, 557, 571, 577, 587, 607, 617, 647, 673, 677, 679, 701, 709, 719, 727, 733, 739, 743, 749, 751 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
799 has divisors 17, 47 and 799, all of which contain the digit 7.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 760], fQ[#, 7] &] (* Robert G. Wilson v, Jun 11 2014 *)
PROG
(Magma) [k:k in [2..800]| forall{d:d in Set(Divisors(k)) diff {1}| 7 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062676, A062677, A062678, A062679, A062680.
KEYWORD
nonn,base,easy
AUTHOR
Erich Friedman, Jul 04 2001
STATUS
approved
A062676 Composite and every divisor (except 1) contains the digit 7. +10
18
497, 679, 749, 799, 1207, 1379, 1739, 1799, 1897, 2479, 2627, 2701, 2779, 3337, 3713, 3997, 4607, 4709, 4711, 4739, 4757, 4907, 5173, 5257, 5327, 5579, 5729, 5767, 5789, 6179, 6749, 6769, 6797, 6887, 6979, 7081, 7169, 7289, 7379, 7597, 7609, 7663 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
799 has divisors 17, 47 and 799, all of which contain the digit 7.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 7670], !PrimeQ[#] && fQ[#, 7] &] (* Robert G. Wilson v, Jun 11 2014 *)
PROG
(Magma) [k:k in [2..8000]| not IsPrime(k) and forall{d:d in Set(Divisors(k)) diff {1}| 7 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062677, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 07 2019
STATUS
approved
A062677 Numbers with property that every divisor (except 1) contains the digit 8. +10
18
83, 89, 181, 281, 283, 383, 389, 487, 587, 683, 787, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 983, 1087, 1181, 1187, 1283, 1289, 1381, 1481, 1483, 1487, 1489, 1583, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Subsequence of A011538, numbers with an 8. - Michel Marcus, Nov 21 2015
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
7387 has divisors 83, 89 and 7387, all of which contain the digit 8.
MAPLE
isA062677 := proc(n)
if n = 1 then
return false;
end if;
for d in numtheory[divisors](n) minus {1} do
convert(convert(d, base, 10), set) ;
if not 8 in % then
return false;
end if;
end do:
true ;
end proc:
for n from 1 to 2000 do
if isA062677(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Mar 27 2017
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1900], fQ[#, 8] &] (* Robert G. Wilson v, Jun 11 2014 *)
CROSSREFS
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062678, A062679, A062680.
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
STATUS
approved
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Last modified August 29 15:03 EDT 2024. Contains 375517 sequences. (Running on oeis4.)