cp's OEIS Frontend

A229321 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 A229321 #17 Jan 16 2018 02:45:10
%S A229321 6,10,15,21,39,110,170,609,897,935,1265,1729,2882,2915,12374,15387,
%T A229321 161833,411230,444797,558830,842741,881705,1091810,1122501,1163990,
%U A229321 1342165,1565565,1898259,2763901,4157605,4453697,4675877,5962835,6241610,6809690,7201599
%N A229321 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 A229321 Subsequence of A120944.
%e A229321 Prime factors of 1265 are 5, 11, 23 and tau(1265) = 8, phi(1265) = 880. 1265 + 880 = 2145 and 2145 / (5 - 8) = -715, 2145 / (11 - 8) = 715, 2145 / (23 - 8) = 143.
%p A229321 with (numtheory); P:=proc(q) global a, b, c, i, ok, p, n;
%p A229321 for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A229321 for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
%p A229321 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 A229321 Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229322-A229324.
%K A229321 nonn
%O A229321 1,1
%A A229321 _Paolo P. Lava_, Sep 20 2013
%E A229321 a(18)-a(37) from _Giovanni Resta_, Sep 20 2013
%E A229321 First term deleted by _Paolo P. Lava_, Sep 23 2013