A318874 - OEIS

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

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OFFSET

1,3

LINKS

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

FORMULA

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

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

EXAMPLE

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.

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 *)

PROG

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

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.

Sequence in context: A225843 A327657 A301957 * A001227 A369466 A060764

Adjacent sequences: A318871 A318872 A318873 * A318875 A318876 A318877

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 05 2018

STATUS

approved