A349374 - OEIS

%I #10 Nov 21 2021 10:17:26

%S 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,

%T 60,34,44,44,126,47,9,90,78,94,48,56,87,106,48,62,174,65,68,110,105,

%U 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

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

%H Antti Karttunen, <a href="/A349374/b349374.txt">Table of n, a(n) for n = 1..20000</a>

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

%t 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 *)

%o (PARI)

%o A003602(n) = (1+(n>>valuation(n,2)))/2;

%o A349374(n) = sumdiv(n,d,A003602(n/d)*core(d));

%Y Cf. A003602, A007913.

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 15 2021