cp's OEIS Frontend

A229322 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 A229322 #16 Jan 16 2018 02:45:15
%S A229322 72285,82218,1612671,52371129,511130199,2111850465,4789685289,
%T A229322 8884216243,8916435021,9863075721,15364177629,28243714821,99459827349
%N A229322 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 A229322 a(15) > 10^11. - _Giovanni Resta_, Sep 20 2013
%C A229322 Subsequence of A120944.
%e A229322 Prime factors of 82218 are 2, 3, 71, 193 and tau(82218) = 16, phi(82218) = 26680. 82218 + 26680 = 109098 and  109098 / (2 + 16) = 6061, 109098 / (3 + 16) = 5742, 109098 / (71 + 16) = 1254, 109098 / (193 + 16) = 522.
%p A229322 with (numtheory); P:=proc(q) global a, b, c, i, ok, p, n;
%p A229322 for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A229322 for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
%p A229322 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 A229322 Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229321, A229323, A229324.
%K A229322 nonn
%O A229322 1,1
%A A229322 _Paolo P. Lava_, Sep 20 2013
%E A229322 a(4)-a(14) from _Giovanni Resta_, Sep 20 2013
%E A229322 First term deleted by _Paolo P. Lava_, Sep 23 2013