cp's OEIS Frontend

A229323 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 A229323 #16 Jan 16 2018 02:45:19
%S A229323 6,10,15,21,42,28101,38505,5298186,8022111,28231629,36367086,98671659,
%T A229323 132798279,163143714,201713946,251860911,434246667,537424773,
%U A229323 968870877,999640581,1495625721,1548129363,3338717307,3836384682,6316358811,6982412973
%N A229323 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 A229323 Subsequence of A120944.
%e A229323 Prime factors of 28101 are 3, 17, 19, 29 and tau(28101) = 16, phi(28101) = 16128. 28101 - 16128 = 11973 and  11973 / (3 - 16) = -921, 11973 / (17 - 16) = 11973, 11973 / (19 - 16) = 3991, 11973 / (29 - 16) = 921.
%p A229323 with (numtheory); P:=proc(q) global a, b, c, i, ok, p, n;
%p A229323 for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A229323 for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
%p A229323 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 A229323 Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229321, A229322, A229324.
%K A229323 nonn
%O A229323 1,1
%A A229323 _Paolo P. Lava_, Sep 20 2013
%E A229323 a(9)-a(27) from _Giovanni Resta_, Sep 20 2013
%E A229323 First term deleted by _Paolo P. Lava_, Sep 23 2013