A369465 - OEIS

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A369465

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

5

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

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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: A325471 A373703 A167155 * A268731 A080219 A339747

Adjacent sequences: A369462 A369463 A369464 * A369466 A369467 A369468

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 27 2024

STATUS

approved