A349570 Dirichlet convolution of A011782 [2^(n-1)] with A055615 (Dirichlet inverse of n).

1, 0, 1, 4, 11, 24, 57, 112, 244, 480, 1013, 1972, 4083, 8064, 16331, 32512, 65519, 130488, 262125, 523244, 1048377, 2095104, 4194281, 8384176, 16777136, 33546240, 67108096, 134201316, 268435427, 536836584, 1073741793, 2147418112, 4294964213, 8589803520, 17179868787, 34359470272, 68719476699, 137438429184, 274877894643

Offset

1,4

Comments

Dirichlet convolution of this sequence with phi (A000010) is A000740, with sigma (A000203) it is A034729, and with A018804 it is A034738.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1001

Formula

a(n) = Sum_{d|n} 2^(d-1) * A055615(n/d).

Mathematica

a[n_] := DivisorSum[n, # * MoebiusMu[#] * 2^(n/# - 1) &]; Array[a, 40] (* Amiram Eldar, Nov 22 2021 *)

Prog

(PARI)
A055615(n) = (n*moebius(n));
A349570(n) = sumdiv(n, d, (2^(d-1)) * A055615(n/d));

Crossrefs

Cf. A011782, A055615, A349569 (Dirichlet inverse).

Cf. also A000010, A000740, A000203, A018804, A034729, A034738, A349564, A349566, A349568.

Sequence in context: A159348 A159349 A349569 * A192597 A181946 A176959

Adjacent sequences: A349567 A349568 A349569 * A349571 A349572 A349573

Keyword

nonn

Author

Antti Karttunen, Nov 22 2021

Status

approved