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

1,6

Links

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

Prog

(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));

Crossrefs

Cf. A001414, A083345.

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

Cf. also A082299, A373362.

Sequence in context: A215010 A136744 A068237 * A083345 A087262 A082343

Adjacent sequences: A373360 A373361 A373362 * A373364 A373365 A373366

Keyword

nonn

Author

Antti Karttunen, Jun 02 2024

Status

approved