A366785 Greatest common divisor of the number of prime factors (counted with multiplicity, A001222) and the greatest prime index (A061395) of n.

0, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 3, 1, 3, 1, 2, 1, 4, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 2, 1, 1, 4, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Author

Antti Karttunen, Oct 23 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A001222, A061395, A340608 (positions of 1's), A360614, A360615.

Programs

PARI

A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
A366785(n) = gcd(bigomega(n), A061395(n));

Formula

a(n) = gcd(A001222(n), A061395(n)).

For n >= 2, a(n) = A001222(n) / A360615(n) = A061395(n) / A360614(n).