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A225707 Composite squarefree numbers n such that p(i)-7 divides n+7, where p(i) are the prime factors of n. 3
33, 65, 165, 209, 345, 713, 1353, 2717, 2945, 4433, 4745, 6149, 7733, 9785, 11297, 16985, 21593, 25265, 26273, 28545, 32357, 35673, 47945, 49913, 55913, 61013, 69113, 69513, 88913, 95465, 106913, 116513, 119009, 121785, 133433, 159185, 167765, 201773 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..50

EXAMPLE

Prime factors of 7733 are 11, 19 and 37. We have that (7733+7)/(11-7) = 1935, (7733+7)/(19-7) = 645 and (7733+7)/(37-7) = 258.

MAPLE

with(numtheory); A225707:=proc(i, j) local c, d, n, ok, p, t;

for n from 1 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: A225707(10^9, 7);

MATHEMATICA

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 7] > 0 && Union[Mod[n + 7, p - 7]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

CROSSREFS

Cf. A208728, A225702-A225706, A225708-A225720.

Sequence in context: A335669 A339908 A071595 * A225511 A248038 A032661

Adjacent sequences:  A225704 A225705 A225706 * A225708 A225709 A225710

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 13 2013

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)