A318875 Number of divisors d of n for which 2*phi(d) < d.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 05 2018

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Maple

A318875 := n -> nops(select(d -> (2*numtheory:-phi(d)) < d, divisors(n))):
seq(A318875(n), n=1..199); # Peter Luschny, Sep 05 2018

Mathematica

A318875[n_] := DivisorSum[n, 1 &, 2*EulerPhi[#] < # &];
Array[A318875, 100] (* Paolo Xausa, Jul 08 2024 *)

PARI

A318875(n) = sumdiv(n,d,(2*eulerphi(d))
				

Formula

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

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