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

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

Offset: 0

Author

Antti Karttunen, May 07 2021

Keywords

• nonn
• look

Comments

Coincides with A344028 on Fibbinary numbers, A003714.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

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

Cf. also A344027, A344028, A344182.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344026(n) = A003415(A005940(1+n));

Formula

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