Search: a062672 -id:a062672
|
|
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
|
|
|
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:
|
|
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
|
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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:])
|
|
CROSSREFS
|
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
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
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
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
|
|
|
LINKS
|
|
|
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;
|
|
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
|
|
|
STATUS
|
approved
|
|
|
Search completed in 0.010 seconds
|