A349374 Dirichlet convolution of Kimberling's paraphrases (A003602) with squarefree part of n (A007913).

1, 3, 5, 4, 8, 15, 11, 6, 12, 24, 17, 20, 20, 33, 42, 7, 26, 36, 29, 32, 58, 51, 35, 30, 29, 60, 34, 44, 44, 126, 47, 9, 90, 78, 94, 48, 56, 87, 106, 48, 62, 174, 65, 68, 110, 105, 71, 35, 54, 87, 138, 80, 80, 102, 146, 66, 154, 132, 89, 168, 92, 141, 153, 10, 172, 270, 101, 104, 186, 282, 107, 72, 110, 168, 167, 116

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A003602, A007913.

Cf. A347954, A347955, A347956, A349136, A349370, A349371, A349372, A349374, A349375, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.

Programs

Mathematica

f[p_, e_] := p^Mod[e, 2]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, k[#] * s[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

PARI

A003602(n) = (1+(n>>valuation(n,2)))/2;
A349374(n) = sumdiv(n,d,A003602(n/d)*core(d));

Formula

a(n) = Sum_{d|n} A003602(n/d) * A007913(d).