A328771 Minimal number of primorials (A002110) that add to A328768(n), where A328768 is the first primorial based variant of arithmetic derivative.

0, 0, 1, 1, 2, 1, 2, 1, 2, 2, 5, 1, 4, 1, 4, 6, 2, 1, 3, 1, 4, 6, 6, 1, 6, 2, 5, 5, 10, 1, 6, 1, 6, 8, 7, 8, 6, 1, 6, 8, 6, 1, 5, 1, 8, 7, 8, 1, 6, 2, 9, 6, 10, 1, 8, 8, 8, 6, 9, 1, 10, 1, 4, 9, 8, 10, 13, 1, 8, 8, 14, 1, 10, 1, 5, 5, 10, 12, 10, 1, 6, 2, 7, 1, 8, 10, 6, 10, 14, 1, 5, 14, 8, 6, 8, 12, 6, 1, 9, 15, 8, 1, 16, 1, 14, 7

Offset: 0

Author

Antti Karttunen, Oct 28 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110, A276150, A324888, A328768, A328772.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A328771(n) = A276150(A328768(n));

Formula

a(n) = A276150(A328768(n)).