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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

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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