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A225715 Composite squarefree numbers n such that p(i)+5 divides n-5, where p(i) are the prime factors of n.

%I A225715 #11 May 17 2013 15:48:21
%S A225715 165,1085,3965,4085,5621,7733,8645,14405,19877,23405,33269,40397,
%T A225715 45365,66929,88949,110885,114917,135005,243941,275621,280085,421085,
%U A225715 439565,455285,460229,474677,480245,496589,505517,518081,570245,706805,709973,900581,912021
%N A225715 Composite squarefree numbers n such that p(i)+5 divides n-5, where p(i) are the prime factors of n.
%H A225715 Paolo P. Lava, <a href="/A225715/b225715.txt">Table of n, a(n) for n = 1..150</a>
%e A225715 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.
%p A225715 with(numtheory); A225715:=proc(i,j) local c, d, n, ok, p, t;
%p A225715 for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p A225715 for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
%p A225715 if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
%p A225715 if ok=1 then print(n); fi; fi; od; end: A225715(10^9,-5);
%t A225715 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 *)
%Y A225715 Cf. A208728, A225702-A225714, A225716-A225720.
%K A225715 nonn
%O A225715 1,1
%A A225715 _Paolo P. Lava_, May 13 2013