A373363 a(n) = gcd(A001414(n), A083345(n)), where A001414 is the sum of prime factors with repetition, and A083345 is the numerator of the sum of the inverses of prime factors with repetition.

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

Offset: 1

Author

Antti Karttunen, Jun 02 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A001414, A083345.

Cf. A345452 (positions of even terms), A353374 (their characteristic function).

Cf. also A082299, A373362.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A373363(n) = gcd(A001414(n), A083345(n));