A318874 Number of divisors d of n for which 2*phi(d) > d.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 05 2018

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

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

Programs

Maple

A318874 := n -> nops(select(d -> (2*numtheory:-phi(d)) > d, divisors(n))):
seq(A318874(n), n=1..99); # Peter Luschny, Sep 05 2018

Mathematica

A318874[n_] := DivisorSum[n, 1 &, 2*EulerPhi[#] > # &];
Array[A318874, 100] (* Paolo Xausa, Jul 08 2024 *)

PARI

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

Formula

a(n) = Sum_{d|n} [A083254(d) > 0].

For all n >= 1, a(n) + A318875(n) + A007814(n) = A000005(n).