A369180 - OEIS

A369180

Alternating sum of the k-adic valuations (ruler functions) of n.

0, 1, -1, 3, -1, 1, -1, 5, -3, 1, -1, 4, -1, 1, -3, 8, -1, 0, -1, 4, -3, 1, -1, 7, -3, 1, -5, 4, -1, 1, -1, 10, -3, 1, -3, 5, -1, 1, -3, 7, -1, 1, -1, 4, -6, 1, -1, 11, -3, 0, -3, 4, -1, -1, -3, 7, -3, 1, -1, 6, -1, 1, -6, 14, -3, 1, -1, 4, -3, 1, -1, 9, -1, 1, -6, 4, -3, 1

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OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = Sum_{k=2..n} (-1)^k * valuation(n,k).

a(n) = A007814(n) - A007949(n) + A235127(n) - (...).

G.f.: Sum_{k>=2, j>=1} (-1)^k x^(k^j)/(1-x^(k^j)).

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{n=1..m} a(n) = log(2).

Dirichlet g.f.: zeta(s) * Sum_{k>=1} (1 - eta(ks)).

Sum_{n>=1} a(n)/n^2 = Pi^2/24.