A342003 Maximal exponent in the prime factorization of the arithmetic derivative of n: a(n) = A051903(A003415(n)).

0, 0, 2, 0, 1, 0, 2, 1, 1, 0, 4, 0, 2, 3, 5, 0, 1, 0, 3, 1, 1, 0, 2, 1, 1, 3, 5, 0, 1, 0, 4, 1, 1, 2, 2, 0, 1, 4, 2, 0, 1, 0, 4, 1, 2, 0, 4, 1, 2, 2, 3, 0, 4, 4, 2, 1, 1, 0, 2, 0, 1, 1, 6, 2, 1, 0, 3, 1, 1, 0, 2, 0, 1, 1, 4, 2, 1, 0, 4, 3, 1, 0, 2, 1, 2, 5, 2, 0, 1, 2, 5, 1, 2, 3, 4, 0, 1, 2, 2, 0, 1, 0, 2, 1

Offset: 2

Author

Antti Karttunen, Mar 01 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537

Crossrefs

Cf. A003415, A051903, A328310, A328311, A328320, A328321, A341994, A341995, A342004.

Cf. A000040 (indices of zeros), A328234 (of ones), A328393 (of the terms < 2).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A342003(n) = A051903(A003415(n));

Formula

a(n) = A051903(A003415(n)).

a(n) = A051903(n) + A328310(n).

a(n) = 1 iff A341994(n) = 1.