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A347955 Dirichlet convolution of A003415 (arithmetic derivative) with A003602 (Kimberling's paraphrases).

%I A347955 #7 Oct 15 2021 21:37:05
%S A347955 0,1,1,5,1,8,1,17,8,11,1,32,1,14,13,49,1,44,1,47,16,20,1,100,13,23,44,
%T A347955 62,1,81,1,129,22,29,19,156,1,32,25,151,1,106,1,92,86,38,1,276,18,92,
%U A347955 31,107,1,206,25,202,34,47,1,301,1,50,111,321,28,156,1,137,40,151,1,460,1,59,120,152,28,181,1,423,206
%N A347955 Dirichlet convolution of A003415 (arithmetic derivative) with A003602 (Kimberling's paraphrases).
%H A347955 Antti Karttunen, <a href="/A347955/b347955.txt">Table of n, a(n) for n = 1..16384</a>
%F A347955 a(n) = Sum_{d|n} A003415(n/d) * A003602(d).
%o A347955 (PARI)
%o A347955 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347955 A003602(n) = (1+(n>>valuation(n,2)))/2;
%o A347955 A347955(n) = sumdiv(n,d,A003415(n/d)*A003602(d));
%Y A347955 Cf. A003415, A003602.
%Y A347955 Cf. also A347954, A347956.
%K A347955 nonn
%O A347955 1,4
%A A347955 _Antti Karttunen_, Sep 20 2021