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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.

%I A225707 #18 May 17 2013 13:19:14
%S A225707 33,65,165,209,345,713,1353,2717,2945,4433,4745,6149,7733,9785,11297,
%T A225707 16985,21593,25265,26273,28545,32357,35673,47945,49913,55913,61013,
%U A225707 69113,69513,88913,95465,106913,116513,119009,121785,133433,159185,167765,201773
%N A225707 Composite squarefree numbers n such that p(i)-7 divides n+7, where p(i) are the prime factors of n.
%H A225707 Paolo P. Lava, <a href="/A225707/b225707.txt">Table of n, a(n) for n = 1..50</a>
%e A225707 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.
%p A225707 with(numtheory); A225707:=proc(i,j) local c, d, n, ok, p, t;
%p A225707 for n from 1 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p A225707 for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
%p A225707 if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
%p A225707 if ok=1 then print(n); fi; fi; od; end: A225707(10^9,7);
%t A225707 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 *)
%Y A225707 Cf. A208728, A225702-A225706, A225708-A225720.
%K A225707 nonn
%O A225707 1,1
%A A225707 _Paolo P. Lava_, May 13 2013