cp's OEIS Frontend

A225705 Composite squarefree numbers n such that p(i)-5 divides n+5, where p(i) are the prime factors of n.

%I A225705 #16 May 17 2013 13:48:01
%S A225705 21,91,187,391,3451,4147,6391,7579,8827,9499,9823,11803,15283,21307,
%T A225705 22243,26887,29563,36091,42763,49387,62491,63427,84091,89947,107707,
%U A225705 116083,126451,139867,155227,227263,270391,287419,302731,317191,320827,376987,381667,433939
%N A225705 Composite squarefree numbers n such that p(i)-5 divides n+5, where p(i) are the prime factors of n.
%H A225705 Paolo P. Lava, <a href="/A225705/b225705.txt">Table of n, a(n) for n = 1..100</a>
%e A225705 Prime factors of 6391 are 7, 11 and 83. We have that (6391+5)/(7-5)  =3198, (6391+5)/(11-5) = 1066 and (6391+5)/(83-5) = 82.
%p A225705 with(numtheory); A225705:=proc(i,j) local c, d, n, ok, p, t;
%p A225705 for n from 1 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p A225705 for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
%p A225705 if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
%p A225705 if ok=1 then print(n); fi; fi; od; end: A225705(10^9,5);
%t A225705 t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 5] > 0 && Union[Mod[n + 5, p - 5]] == {0}, AppendTo[t, n]]]; t (* _T. D. Noe_, May 17 2013 *)
%Y A225705 Cf. A208728, A225702-A225704, A225706-A225720.
%K A225705 nonn
%O A225705 1,1
%A A225705 _Paolo P. Lava_, May 13 2013