A389453 Arithmetic derivative of the largest p-full divisor of n (a term of A054744 that divides n).

0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 32, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 27, 4, 0, 0, 0, 80, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 32, 0, 0, 0, 4, 0, 27, 0, 12, 0, 0, 0, 4, 0, 0, 0, 192, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 32, 108, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 80, 0, 0, 0, 4

Offset

1,4

Links

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

Formula

a(n) = A003415(A368333(n)).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A389455(n) = { my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] < f[i, 1], f[i, 1]^f[i, 2], 1)); }
A389453(n) = A003415(n/A389455(n));

Crossrefs

Cf. A003415, A048103 (positions of 0's), A054744, A368333, A389454, A389455.

Sequence in context: A046782 A074037 A285132 * A239261 A391569 A395300

Adjacent sequences: A389450 A389451 A389452 * A389454 A389455 A389456

Keyword

nonn

Author

Antti Karttunen, Oct 04 2025

Status

approved