A368405 Infinitary version of Mertens's function: a(n) = Sum_{k=1..n} A064179(k).

1, 0, -1, -2, -3, -2, -3, -2, -3, -2, -3, -2, -3, -2, -1, -2, -3, -2, -3, -2, -1, 0, -1, -2, -3, -2, -1, 0, -1, -2, -3, -2, -1, 0, 1, 2, 1, 2, 3, 2, 1, 0, -1, 0, 1, 2, 1, 2, 1, 2, 3, 4, 3, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5

Offset: 1

Author

Amiram Eldar, Dec 23 2023

Keywords

• sign
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Rasa Steuding, Jörn Steuding, and László Tóth, A modified Möbius mu-function, Rendiconti del Circolo Matematico di Palermo, Vol. 60 (2011), pp. 13-21; arXiv preprint, arXiv:1109.4242 [math.NT], 2011.

Crossrefs

Partial sums of A064179.

Similar sequences: A002321, A174863 (unitary), A209802 (exponential).

Programs

Mathematica

f[p_, e_] := (-1)^DigitCount[e, 2, 1]; imu[1] = 1; imu[n_] := Times @@ f @@@ FactorInteger[n]; Accumulate[Array[imu, 100]]

PARI

imu(n) = vecprod(apply(x -> (-1)^hammingweight(x), factor(n)[, 2]));
lista(nmax) = {my(s = 0); for(k = 1, nmax, s+ = imu(k); print1(s, ", "));}