A341472 Partial sums of A341444.

1, -1, -3, -1, -3, 2, 0, -2, 0, 5, 3, -4, -6, -1, 4, 6, 4, -3, -5, -12, -7, -2, -4, 5, 7, 12, 10, 3, 1, -15, -17, -19, -14, -9, -4, 10, 8, 13, 18, 27, 25, 9, 7, 0, -7, -2, -4, -15, -13, -20, -15, -22, -24, -15, -10, -1, 4, 9, 7, 37, 35, 40, 33, 35, 40, 24, 22, 15, 20, 4

Offset

1,3

Comments

This is G^(-1) in Schmidt article.

Links

Table of n, a(n) for n=1..70.

M. D. Schmidt, New characterizations of the summatory function of the Moebius function, arXiv:2102.05842 [math.NT], 2021.

Prog

(PARI) cOmega(n) = if (n==1, 1, my(f=factor(n)); bigomega(n)!*prod(k=1, #f~, 1/f[k, 2]!)); \\ A008480
gm(n) = (-1)^bigomega(n)*sumdiv(n, d, moebius(n/d)^2*cOmega(d)); \\ A341444
a(n) = sum(k=1, n, gm(k));

Crossrefs

Cf. A341444.

Sequence in context: A099906 A262026 A270390 * A047787 A102668 A243848

Adjacent sequences: A341469 A341470 A341471 * A341473 A341474 A341475

Keyword

sign

Author

Michel Marcus, Feb 13 2021

Status

approved