A327928 - OEIS

A327928

Number of distinct primes p such that p^p divides the arithmetic derivative of n.

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0

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OFFSET

0,82

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

FORMULA

a(0) = a(1) = 0; for n > 1, a(n) = A129251(A003415(n)).

EXAMPLE

For n=20, A003415(20) = 24 = 2^3 * 3^1, thus only 2^2 divides 24, and a(24) = 1.

For n=81, A003415(81) = 108 = 2^2 * 3^3. Both 2^2 and 3^3 divide 108, thus a(81) = 2.

PROG

(PARI)