cp's OEIS Frontend

A225703 Composite squarefree numbers n such that p(i)-3 divides n+3, where p(i) are the prime factors of n.

%I A225703 #12 May 17 2013 14:11:10
%S A225703 77,2717,3245,18221,30797,37177,46397,51997,56573,61997,111757,128573,
%T A225703 149765,158197,263117,264517,314717,437437,475157,617437,667573,
%U A225703 683537,701005,718333,834197,864497,902957,904397,929005,945277,1030237,1096205,1139653,1188317
%N A225703 Composite squarefree numbers n such that p(i)-3 divides n+3, where p(i) are the prime factors of n.
%H A225703 Paolo P. Lava, <a href="/A225703/b225703.txt">Table of n, a(n) for n = 1..80</a>
%e A225703 Prime factors of 37177 are 7, 47 and 113. We have that (37177+3)/(7-3) = 9295, (37177+3)/(47-3) = 845 and (37177+3)/(113-3) = 338.
%p A225703 with(numtheory); A225703:=proc(i,j) local c, d, n, ok, p, t;
%p A225703 for n from 1 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p A225703 for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
%p A225703 if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
%p A225703 if ok=1 then print(n); fi; fi; od; end: A225703(10^9,3);
%t A225703 t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 3] > 0 && Union[Mod[n + 3, p - 3]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* _T. D. Noe_, May 17 2013 *)
%Y A225703 Cf. A208728, A225702, A225704-A225720.
%K A225703 nonn
%O A225703 1,1
%A A225703 _Paolo P. Lava_, May 13 2013