A373378 a(n) = gcd(A003415(n), A059975(n)), where A003415 is the arithmetic derivative and A059975 is fully additive with a(p) = p-1.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 1, 1, 2, 4, 1, 1, 1, 6, 2, 1, 1, 1, 2, 1, 3, 8, 1, 1, 1, 5, 2, 1, 2, 6, 1, 1, 2, 1, 1, 1, 1, 12, 1, 1, 1, 2, 2, 9, 2, 14, 1, 1, 2, 1, 2, 1, 1, 4, 1, 1, 1, 6, 2, 1, 1, 18, 2, 1, 1, 1, 1, 1, 5, 20, 2, 1, 1, 8, 4, 1, 1, 2, 2, 1, 2, 1, 1, 3, 2, 24, 2, 1, 2, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Jun 05 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A059975.

Cf. A368998 (positions of even terms), A368999 (of odd terms).

Cf. also A373364, A373368, A373369, A373377.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A059975(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };
A373378(n) = gcd(A003415(n), A059975(n));

Formula

For n >= 1, a(n) is a multiple of A373377(n).