A295521 a(n) = (1/n) * Sum_{d|n} mu(n/d)*(4^d - 3^d - 2^d + 1).

0, 2, 10, 39, 150, 545, 2010, 7320, 26880, 98775, 365010, 1353185, 5038950, 18830145, 70623958, 265737270, 1002976350, 3796197160, 14406059010, 54801140307, 208932573650, 798218035245, 3055417070010, 11716354754030, 45002103387120, 173117601112575

Offset: 1

Author

Seiichi Manyama, Nov 23 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1666
• Wikipedia, Möbius function

Crossrefs

Cf. A001037, A008683, A020988, A027376, A027377.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * (4^# - 3^# - 2^# + 1) &] / n; Array[a, 26] (* Amiram Eldar, Oct 04 2023 *)

PARI

{a(n) = sumdiv(n, d, moebius(n/d)*(4^d-3^d-2^d+1))/n}

Formula

a(n) = A027377(n) - A027376(n) - A001037(n) for n > 1.