A225716 -id:A225716

Search: a225716 -id:a225716

Displaying 1-2 of 2 results found.

page 1

A225715

Composite squarefree numbers n such that p(i)+5 divides n-5, where p(i) are the prime factors of n.

+10
3

165, 1085, 3965, 4085, 5621, 7733, 8645, 14405, 19877, 23405, 33269, 40397, 45365, 66929, 88949, 110885, 114917, 135005, 243941, 275621, 280085, 421085, 439565, 455285, 460229, 474677, 480245, 496589, 505517, 518081, 570245, 706805, 709973, 900581, 912021

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..150

EXAMPLE

Prime factors of 7733 are 11, 19 and 37. We have that (7733-5)/(11+5) = 483, (7733-5)/(19+5) = 322 and (7733-5)/(37+5) = 184.

MAPLE

with(numtheory); A225715:=proc(i, j) local c, d, n, ok, p, t;

for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;

for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;

if not type((n+j)/(p[d][1]-j), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); fi; fi; od; end: A225715(10^9, -5);

MATHEMATICA

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 5, p + 5]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

CROSSREFS

Cf. A208728, A225702-A225714, A225716-A225720.

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 13 2013

STATUS

approved

A225717

Composite squarefree numbers n such that p(i)+7 divides n-7, where p(i) are the prime factors of n.

+10
3

1015, 4147, 7567, 9367, 13447, 15847, 25543, 29127, 33847, 39319, 40807, 58327, 80647, 87607, 116071, 135439, 139867, 145915, 177415, 186667, 190747, 203287, 222343, 253897, 321127, 356167, 380887, 384391, 391207, 403495, 453607, 470587, 501607, 602167, 606535

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100

EXAMPLE

Prime factors of 15847 are 13, 23 and 53. We have that (15847-7)/(13+7) = 792, (15847-7)/(23+7) = 528 and (15847-7)/(53+7) = 264.

MAPLE

with(numtheory); A225717:=proc(i, j) local c, d, n, ok, p, t;

for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;

for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;

if not type((n+j)/(p[d][1]-j), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); fi; fi; od; end: A225717(10^9, -7);

MATHEMATICA

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 7, p + 7]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

CROSSREFS

Cf. A208728, A225702-A225716, A225718-A225720.

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 13 2013

STATUS

approved

page 1

Search completed in 0.008 seconds