A344210 a(n) = Sum_{d|n} mu(n/d) * d^n / phi(n).

1, 3, 13, 120, 781, 22932, 137257, 4177920, 64566801, 2497558338, 28531167061, 2228476723200, 25239592216021, 1851888100411464, 54736732481116543, 2305807824841605120, 51702516367896047761, 6557709646516945221396, 109912203092239643840221

Offset: 1

Author

Seiichi Manyama, May 12 2021

Keywords

• nonn

Crossrefs

Main diagonal of A263950.

Cf. A000010, A067858, A008683, A000203.

Programs

Mathematica

Table[DivisorSum[n,MoebiusMu[n/#]*#^n/EulerPhi[n]&],{n,20}] (* Giorgos Kalogeropoulos, May 13 2021 *)

PARI

a(n) = sumdiv(n, d, moebius(n/d)*d^n)/eulerphi(n);

Formula

a(n) = J_n(n) / phi(n) = A067858(n) / A000010(n).

a(n) = (1/n) * Sum_{d|n} mu(n/d)*sigma(d^n). - Ridouane Oudra, Apr 03 2025