A365461 Sum of digits when A181821(n) is written in primorial base (A049345).

1, 1, 2, 1, 2, 2, 4, 1, 2, 4, 2, 2, 4, 4, 4, 1, 6, 6, 6, 4, 8, 4, 6, 2, 2, 8, 6, 2, 12, 6, 16, 1, 6, 10, 4, 6, 16, 10, 8, 4, 10, 6, 10, 4, 12, 10, 6, 2, 8, 6, 10, 8, 12, 10, 8, 8, 20, 10, 18, 2, 26, 14, 8, 1, 12, 12, 22, 10, 20, 12, 28, 6, 28, 14, 10, 10, 6, 8, 34, 4, 8, 18, 38, 4, 10, 14, 20, 6, 52, 10, 12, 10, 24

Offset: 1

Author

Antti Karttunen, Sep 15 2023

Keywords

• nonn

Comments

Minimal number of primorials (A002110) that add to A181821(n).

Links

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

Crossrefs

Cf. A002110, A049345, A122111, A181821, A276150, A324888, A365460.

Programs

PARI

A181821(n) = { my(f=factor(n),p=0,m=1); forstep(i=#f~,1,-1,while(f[i,2], f[i,2]--; m *= (p=nextprime(p+1))^primepi(f[i,1]))); (m); };
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A365461(n) = A276150(A181821(n));

Formula

a(n) = A276150(A181821(n)).

a(n) = A324888(A122111(n)).

a(n) >= A365460(n).