A373249 a(n) = A181819(n) / gcd(n, A181819(n)), where A181819(n) is the prime shadow of n.

1, 1, 2, 3, 2, 2, 2, 5, 1, 2, 2, 1, 2, 2, 4, 7, 2, 1, 2, 3, 4, 2, 2, 5, 3, 2, 5, 3, 2, 4, 2, 11, 4, 2, 4, 1, 2, 2, 4, 1, 2, 4, 2, 3, 2, 2, 2, 7, 3, 3, 4, 3, 2, 5, 4, 5, 4, 2, 2, 1, 2, 2, 2, 13, 4, 4, 2, 3, 4, 4, 2, 5, 2, 2, 2, 3, 4, 4, 2, 7, 7, 2, 2, 1, 4, 2, 4, 5, 2, 2, 4, 3, 4, 2, 4, 11, 2, 3, 2, 9, 2, 4, 2, 5, 8

Offset: 1

Author

Antti Karttunen, May 30 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A181819, A373246.

Cf. A325755 (positions of 1's), A353566 (their characteristic function).

Programs

PARI

A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A373249(n) = { my(s=A181819(n)); s/gcd(n, s); };

Formula

a(n) = A181819(n) / A373246(n) = A181819(n) / gcd(n, A181819(n)).