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A369465 Arithmetic derivative of the odd part of n: a(n) = A003415(A000265(n)).

%I A369465 #8 Jan 27 2024 18:51:23
%S A369465 0,0,1,0,1,1,1,0,6,1,1,1,1,1,8,0,1,6,1,1,10,1,1,1,10,1,27,1,1,8,1,0,
%T A369465 14,1,12,6,1,1,16,1,1,10,1,1,39,1,1,1,14,10,20,1,1,27,16,1,22,1,1,8,1,
%U A369465 1,51,0,18,14,1,1,26,12,1,6,1,1,55,1,18,16,1,1,108,1,1,10,22,1,32,1,1,39,20,1,34,1,24
%N A369465 Arithmetic derivative of the odd part of n: a(n) = A003415(A000265(n)).
%H A369465 Antti Karttunen, <a href="/A369465/b369465.txt">Table of n, a(n) for n = 1..16384</a>
%F A369465 a(n) = A003415(A000265(n)) = A349905(A064989(n)).
%o A369465 (PARI)
%o A369465 A000265(n) = (n>>valuation(n,2));
%o A369465 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369465 A369465(n) = A003415(A000265(n));
%Y A369465 Cf. A000265, A003415, A064989, A349905, A369466 (rgs-transform).
%Y A369465 Cf. also A369449.
%K A369465 nonn
%O A369465 1,9
%A A369465 _Antti Karttunen_, Jan 27 2024