A371090 Additive with a(p^1) = 1, a(p^e) = a(A276086(e)) for e > 1, where A276086 is the primorial base exp-function.

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

Offset: 1

Author

Antti Karttunen, Mar 31 2024

Keywords

• nonn

Comments

Used to construct A371091.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001221, A001222, A276086, A371091.

Differs from A064547 for the first time at n=63, where a(64) = 1, while A064547(64) = 2.

Differs from A058061 for the first time at n=128, where a(128) = 2, while A058061(128) = 3.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A371090(n) = vecsum(apply(e->if(1==e,1,A371090(A276086(e))),factor(n)[, 2]));

Formula

Additive with a(p^1) = 1, a(p^e) = A371091(e) for e > 1.

For all n >= 1, A001221(n) <= a(n) <= A001222(n).