A344026 - OEIS

%I #16 May 18 2021 07:24:32

%S 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 60,75,81,108,80,1,13,14,32,16,41,51,68,18,59,71,92,95,123,162,112,22,

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

%C Coincides with A344028 on Fibbinary numbers, A003714.

%H Antti Karttunen, <a href="/A344026/b344026.txt">Table of n, a(n) for n = 0..8192</a>

%H Antti Karttunen, <a href="/A344026/a344026.txt">Data supplement: n, a(n) computed for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(2^n) = 1 for all n >= 0.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A344026(n) = A003415(A005940(1+n));

%Y Cf. A000079 (positions of ones), A003415, A003714, A005940.

%Y Cf. also A344027, A344028, A344182.

%K nonn,look

%O 0,4

%A _Antti Karttunen_, May 07 2021