A349570 - OEIS

A349570

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

%I #14 Jan 09 2024 13:19:42

%S 1,0,1,4,11,24,57,112,244,480,1013,1972,4083,8064,16331,32512,65519,

%T 130488,262125,523244,1048377,2095104,4194281,8384176,16777136,

%U 33546240,67108096,134201316,268435427,536836584,1073741793,2147418112,4294964213,8589803520,17179868787,34359470272,68719476699,137438429184,274877894643

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

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

%H Antti Karttunen, <a href="/A349570/b349570.txt">Table of n, a(n) for n = 1..1001</a>

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

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

%o (PARI)

%o A055615(n) = (n*moebius(n));

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

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

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

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 22 2021