A225707 Composite squarefree numbers n such that p(i)-7 divides n+7, where p(i) are the prime factors of n.

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

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