%I #14 Jul 08 2024 10:40:54

%S 1,1,2,1,2,2,2,1,3,2,2,2,2,2,4,1,2,3,2,2,4,2,2,2,3,2,4,2,2,4,2,1,4,2,

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

%U 4,4,2,3,2,2,6,2,4,4,2,2,5,2,2,4,4,2,4,2,2,6,4,2,4,2,4,2,2,3,6,3,2,4,2,2,7

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

%H Antti Karttunen, <a href="/A318874/b318874.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) + A318875(n) + A007814(n) = A000005(n).

%e n = 105 has eight divisors: [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, we obtain [1, 1, 3, 5, 1, 3, 13, -9], and seven of these numbers are positive, thus a(105) = 7.

%p A318874 := n -> nops(select(d -> (2*numtheory:-phi(d)) > d, divisors(n))):

%p seq(A318874(n), n=1..99); # _Peter Luschny_, Sep 05 2018

%t A318874[n_] := DivisorSum[n, 1 &, 2*EulerPhi[#] > # &];

%t Array[A318874, 100] (* _Paolo Xausa_, Jul 08 2024 *)

%o (PARI) A318874(n) = sumdiv(n,d,(2*eulerphi(d))>d);

%Y Cf. A000010, A083254, A318875, A318876, A318878.

%Y Differs from A001227 for the first time at n=105, where a(105) = 7, while A001227(105) = 8.

%K nonn

%O 1,3

%A _Antti Karttunen_, Sep 05 2018