A091555 Partial sums of Mertens's function (A002321).

1, 1, 0, -1, -3, -4, -6, -8, -10, -11, -13, -15, -18, -20, -21, -22, -24, -26, -29, -32, -34, -35, -37, -39, -41, -42, -43, -44, -46, -49, -53, -57, -60, -62, -63, -64, -66, -67, -67, -67, -68, -70, -73, -76, -79, -81, -84, -87, -90, -93, -95, -97, -100, -103, -105, -107

Offset: 1

Author

Jon Perry, Mar 04 2004

Keywords

• sign

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A002321, A008683.

Programs

Mathematica

Table[Sum[MoebiusMu[k] (n - k + 1), {k, 1, n}], {n , 1, 56}] (* Indranil Ghosh, Mar 16 2017 *)
Accumulate[Table[Sum[MoebiusMu[k], {k, 1, n}], {n, 1, 100}]] (* Vaclav Kotesovec, Nov 30 2024 *)

PARI

for(n=1, 56, print1(sum(k=1, n, moebius(k) * (n - k + 1)),", ")) \\ Indranil Ghosh, Mar 16 2017

Formula

a(n) = Sum_{k=1..n} mu(k)*(n-k+1) where mu=A008683, the Moebius function. - Reinhard Zumkeller, Nov 06 2006

G.f.: (1/(1 - x)^2)*Sum_{k>=1} mu(k)*x^k. - Ilya Gutkovskiy, Mar 11 2018

Extensions

More terms from Reinhard Zumkeller, Nov 06 2006