%I #12 May 17 2013 15:50:00

%S 1015,4147,7567,9367,13447,15847,25543,29127,33847,39319,40807,58327,

%T 80647,87607,116071,135439,139867,145915,177415,186667,190747,203287,

%U 222343,253897,321127,356167,380887,384391,391207,403495,453607,470587,501607,602167,606535

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

%H Paolo P. Lava, <a href="/A225717/b225717.txt">Table of n, a(n) for n = 1..100</a>

%e 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.

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

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

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

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

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

%t 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 *)

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

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 13 2013