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

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, 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, 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

Offset

1,9

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A003415(A000265(n)) = A349905(A064989(n)).

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369465(n) = A003415(A000265(n));

Crossrefs

Cf. A000265, A003415, A064989, A349905, A369466 (rgs-transform).

Cf. also A369449.

Sequence in context: A234959 A325471 A167155 * A268731 A080219 A339747

Adjacent sequences: A369462 A369463 A369464 * A369466 A369467 A369468

Keyword

nonn

Author

Antti Karttunen, Jan 27 2024

Status

approved