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A347129 a(n) = A347130(n) / A003557(n), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n.

%I A347129 #12 Aug 26 2021 16:07:42
%S A347129 0,1,1,3,1,10,1,6,3,14,1,24,1,18,16,10,1,21,1,36,20,26,1,44,3,30,6,48,
%T A347129 1,124,1,15,28,38,24,45,1,42,32,68,1,164,1,72,39,50,1,70,3,27,40,84,1,
%U A347129 36,32,92,44,62,1,276,1,66,51,21,36,244,1,108,52,236,1,78,1,78,33,120,36,284,1,110,10,86,1,372,44
%N A347129 a(n) = A347130(n) / A003557(n), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n.
%H A347129 Antti Karttunen, <a href="/A347129/b347129.txt">Table of n, a(n) for n = 1..10080</a>
%H A347129 Antti Karttunen, <a href="/A347129/a347129.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A347129 a(n) = A347130(n) / A003557(n).
%o A347129 (PARI)
%o A347129 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347129 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A347129 A347130(n) = sumdiv(n,d,d*A003415(n/d));
%o A347129 A347129(n) = (A347130(n) / A003557(n));
%Y A347129 Cf. A003415, A003557, A347126 [= a(A276086(n))], A347130.
%Y A347129 Cf. also A342001, A347127, A347128.
%K A347129 nonn
%O A347129 1,4
%A A347129 _Antti Karttunen_, Aug 23 2021