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

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

Prog

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

Sequence in context: A212178 A322818 A362611 * A353507 A362613 A327500

Adjacent sequences: A374467 A374468 A374469 * A374471 A374472 A374473

Keyword

nonn

Author

Antti Karttunen, Jul 14 2024

Status

approved