A297381 Numerator of -A023900(n)/2.

-1, 1, 1, 1, 2, -1, 3, 1, 1, -2, 5, -1, 6, -3, -4, 1, 8, -1, 9, -2, -6, -5, 11, -1, 2, -6, 1, -3, 14, 4, 15, 1, -10, -8, -12, -1, 18, -9, -12, -2, 20, 6, 21, -5, -4, -11, 23, -1, 3, -2, -16, -6, 26, -1, -20, -3, -18, -14, 29, 4, 30, -15, -6, 1, -24, 10, 33, -8, -22, 12, 35, -1, 36, -18, -4, -9, -30, 12, 39, -2, 1, -20, 41, 6, -32, -21, -28, -5

Offset: 1

Author

Mats Granvik, Dec 29 2017

Keywords

• sign
• frac

Links

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

Crossrefs

Cf. A023900, A297382 (denominators).

Programs

Mathematica

Clear[n, s, nn]; nn = 64; Numerator[Table[Limit[Zeta[s]*Total[MoebiusMu[Divisors[n]]/Divisors[n]^(s - 1)], s -> 0], {n, 1, nn}]]

PARI

a(n) = numerator(-sumdiv(n, d, d*moebius(d))/2) \\ Iain Fox, Dec 29 2017

PARI

A297381(n) = numerator(-(1/2)*factorback(apply(p -> 1-p, factor(n)[, 1]))); \\ Antti Karttunen, Sep 30 2018

Formula

a(n) = numerator of -A023900(n)/2.

a(n) = numerator of lim_{s->0} zeta(s)*Sum_{d|n} A008683(d)/d^(s-1).

a(n) = numerator of lim_{N->infinity} (1/N)*Sum_{m=1..N} Sum_{k=1..m} A191898(n, k) for n > 1.

a(k) = numerators of lim_{N->infinity} (1/N)*Sum_{m=1..N} Sum_{n=1..m} A191898(n, k) for k > 1.

Extensions

More terms from Antti Karttunen, Sep 30 2018