A318875 - OEIS

%I #13 Jul 08 2024 10:40:57

%S 0,0,0,0,0,1,0,0,0,1,0,2,0,1,0,0,0,2,0,2,0,1,0,3,0,1,0,2,0,3,0,0,0,1,

%T 0,4,0,1,0,3,0,3,0,2,0,1,0,4,0,2,0,2,0,3,0,3,0,1,0,6,0,1,0,0,0,3,0,2,

%U 0,3,0,6,0,1,0,2,0,3,0,4,0,1,0,6,0,1,0,3,0,5,0,2,0,1,0,5,0,2,0,4,0,3,0,3,1

%N Number of divisors d of n for which 2*phi(d) < d.

%H Antti Karttunen, <a href="/A318875/b318875.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} [A083254(d) < 0].

%F For all n >= 1, a(n) + A318874(n) + A007814(n) = A000005(n).

%p A318875 := n -> nops(select(d -> (2*numtheory:-phi(d)) < d, divisors(n))):

%p seq(A318875(n), n=1..199); # _Peter Luschny_, Sep 05 2018

%t A318875[n_] := DivisorSum[n, 1 &, 2*EulerPhi[#] < # &];

%t Array[A318875, 100] (* _Paolo Xausa_, Jul 08 2024 *)

%o (PARI) A318875(n) = sumdiv(n,d,(2*eulerphi(d))<d);

%Y Cf. A000010, A083254, A318874, A318877, A318879.

%K nonn

%O 1,12

%A _Antti Karttunen_, Sep 05 2018