A373377 a(n) = gcd(A059975(n), A083345(n)), where A059975 is fully additive with a(p) = p-1, and A083345 is the numerator of the fully additive function with a(p) = 1/p.

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

Offset

1,8

Comments

For each n >= 2, a(n) is a divisor of A373378(n).

Links

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

Prog

(PARI)
A059975(n) = { my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A373377(n) = gcd(A059975(n), A083345(n));

Crossrefs

Cf. A059975, A083345.

Cf. A369002 (positions of even terms), A369003 (of odd terms).

Cf. also A373363, A373368, A373369, A373378.

Sequence in context: A197027 A143772 A373366 * A053989 A342459 A057160

Adjacent sequences: A373374 A373375 A373376 * A373378 A373379 A373380

Keyword

nonn

Author

Antti Karttunen, Jun 05 2024

Status

approved