A349375 Dirichlet convolution of Kimberling's paraphrases (A003602) with Liouville's lambda.

1, 0, 1, 1, 2, 0, 3, 0, 4, 0, 5, 1, 6, 0, 4, 1, 8, 0, 9, 2, 6, 0, 11, 0, 11, 0, 10, 3, 14, 0, 15, 0, 10, 0, 12, 4, 18, 0, 12, 0, 20, 0, 21, 5, 14, 0, 23, 1, 22, 0, 16, 6, 26, 0, 20, 0, 18, 0, 29, 4, 30, 0, 21, 1, 24, 0, 33, 8, 22, 0, 35, 0, 36, 0, 21, 9, 30, 0, 39, 2, 31, 0, 41, 6, 32, 0, 28, 0, 44, 0, 36, 11, 30, 0, 36

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} A003602(n/d) * A008836(d).

Mathematica

k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, k[#] * LiouvilleLambda[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

Prog

(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A008836(n) = ((-1)^bigomega(n));
A349375(n) = sumdiv(n, d, A003602(n/d)*A008836(d));

Crossrefs

Cf. A003602, A008836.

Cf. A347954, A347955, A347956, A349136, A349370, A349371, A349372, A349373, A349374, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.

Cf. also A349395.

Sequence in context: A008723 A263397 A008803 * A008722 A008736 A263396

Adjacent sequences: A349372 A349373 A349374 * A349376 A349377 A349378

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved