A373364 a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.

0, 1, 1, 4, 1, 5, 1, 6, 6, 7, 1, 1, 1, 9, 8, 8, 1, 1, 1, 3, 10, 13, 1, 1, 10, 15, 9, 1, 1, 1, 1, 10, 14, 19, 12, 10, 1, 21, 16, 1, 1, 1, 1, 3, 1, 25, 1, 1, 14, 3, 20, 1, 1, 1, 16, 1, 22, 31, 1, 4, 1, 33, 1, 12, 18, 1, 1, 3, 26, 1, 1, 12, 1, 39, 1, 1, 18, 1, 1, 1, 12, 43, 1, 2, 22, 45, 32, 1, 1, 1, 20, 3, 34, 49, 24

Offset: 1

Author

Antti Karttunen, Jun 02 2024

Keywords

• nonn

Comments

For n >= 1, a(n) is a multiple of A373363(n).

Links

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

Crossrefs

Cf. A001414, A003415, A373375 (positions of even terms), A373376 (of odd terms).

Cf. also A082299, A373362, A373363.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373364(n) = gcd(A001414(n), A003415(n));