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A344026 Arithmetic derivative applied to the Doudna sequence: a(n) = A003415(A005940(1+n)).

%I A344026 #16 May 18 2021 07:24:32
%S A344026 0,1,1,4,1,5,6,12,1,7,8,16,10,21,27,32,1,9,10,24,12,31,39,44,14,45,55,
%T A344026 60,75,81,108,80,1,13,14,32,16,41,51,68,18,59,71,92,95,123,162,112,22,
%U A344026 77,91,140,119,185,240,156,147,275,350,216,500,297,405,192,1,15,16,48,18,61,75,92,20,87,103,124,135,165,216
%N A344026 Arithmetic derivative applied to the Doudna sequence: a(n) = A003415(A005940(1+n)).
%C A344026 Coincides with A344028 on Fibbinary numbers, A003714.
%H A344026 Antti Karttunen, <a href="/A344026/b344026.txt">Table of n, a(n) for n = 0..8192</a>
%H A344026 Antti Karttunen, <a href="/A344026/a344026.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A344026 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A344026 a(2^n) = 1 for all n >= 0.
%o A344026 (PARI)
%o A344026 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A344026 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A344026 A344026(n) = A003415(A005940(1+n));
%Y A344026 Cf. A000079 (positions of ones), A003415, A003714, A005940.
%Y A344026 Cf. also A344027, A344028, A344182.
%K A344026 nonn,look
%O A344026 0,4
%A A344026 _Antti Karttunen_, May 07 2021