cp's OEIS Frontend

A229324 Composite squarefree numbers n such that p + tau(n) divides n - phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).

%I A229324 #20 Oct 01 2013 04:41:37
%S A229324 115,205,295,565,655,745,835,1195,1285,1465,1555,1735,1915,2005,2095,
%T A229324 2455,2545,2815,2995,3085,3265,3715,3805,3985,4435,4705,4885,5065,
%U A229324 5155,5245,5515,5965,6145,6415,6505,6595,6865,7045,7135,7405,7495,7765,7855,8035
%N A229324 Composite squarefree numbers n such that p + tau(n) divides n - phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).
%C A229324 All terms are apparently multiple of 5.
%C A229324 It appears that a(n) = 5*A061240(n+1). - _Michel Marcus_, Sep 21 2013
%H A229324 Paolo P. Lava, <a href="/A229324/b229324.txt">Table of n, a(n) for n = 1..500</a>
%e A229324 Prime factors of 2815 are 5, 563 and tau(2815) = 4, phi(2815) = 2248. 2815 - 2248 = 567 and  567 / (5 + 4) = 63, 567 / (563 + 4) = 1.
%p A229324 with (numtheory); P:=proc(q) global a, b, c, i, ok, p, n;
%p A229324 for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A229324 for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
%p A229324 else if not type((n-phi(n))/(a[i][1]+tau(n)),integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(6*10^9);
%Y A229324 Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229321-A229323.
%K A229324 nonn
%O A229324 1,1
%A A229324 _Paolo P. Lava_, Sep 20 2013
%E A229324 Deleted first term, changed b-file and comment by _Paolo P. Lava_, Sep 23 2013