A373365 a(n) = gcd(A001414(n), A064097(n)), where A001414 is the sum of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 3, 1, 1, 2, 1, 5, 7, 1, 1, 2, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 8, 1, 2, 1, 1, 1, 1, 1, 1, 6, 2, 8, 1, 7, 1, 2, 1, 1, 1, 1, 1, 1, 9, 2, 1, 1, 4, 1, 1, 2, 2, 9, 1, 1, 1, 1, 1, 9, 1, 1, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3

Offset: 1

Author

Antti Karttunen, Jun 02 2024

Keywords

• nonn

Comments

As A001414 and A064097 are both fully additive sequences, all sequences that give the positions of multiples of some k > 1 in this sequence are closed under multiplication.

Links

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

Crossrefs

Cf. A001414, A064097.

Cf. also A082299, A373362, A373363, A373364, A373366.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A064097(n) = if(1==n,0,1+A064097(n-(n/vecmin(factor(n)[,1]))));
A373365(n) = gcd(A001414(n), A064097(n));