A374470 a(n) = gcd(bigomega(n), A064547(n)), where A064547 is the count of 1-bits in the exponents of the prime factorization of n, and bigomega is the number of prime factors of n (with multiplicity).

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

Offset: 1

Author

Antti Karttunen, Jul 14 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001222, A064547, A374471, A374472 (indices of even terms), A374473 (of odd terms).

Differs from A327500, A362613, A351946, A353507 first at n=60, where a(60) = 1.

Differs from A362611 first at n=64, where a(64) = 2, while A362611(64) = 1.

Programs

PARI

A064547(n) = { my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); };
A374470(n) = gcd(bigomega(n),A064547(n));