A353496 The arithmetic derivative of the largest proper divisor of n, reduced modulo 4, with a(1) = 0.

0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 3, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 3, 0, 3, 1, 0, 1, 1, 0, 3, 0, 1, 2, 0, 1, 2, 0, 3, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 3, 1, 0, 1, 1, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0

Offset: 1

Author

Antti Karttunen, Apr 26 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A010873, A032742, A353493.

Cf. also A353490.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A353496(n) = (A003415(A032742(n))%4);

Formula

a(n) = A353493(A032742(n)) = A010873(A003415(A032742(n))).