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

1,4

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.

Mathematica

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

Prog

(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, ", ")); }

Crossrefs

Partial sums of A064179.

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

Sequence in context: A307200 A339092 A165587 * A356464 A010693 A158478

Adjacent sequences: A368402 A368403 A368404 * A368406 A368407 A368408

Keyword

sign,easy

Author

Amiram Eldar, Dec 23 2023

Status

approved