A328772 Minimal number of primorials (A002110) that add to A328769(n), where A328769 is the second primorial based variant of arithmetic derivative.

0, 0, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 4, 1, 5, 4, 4, 1, 3, 1, 8, 6, 7, 1, 4, 4, 7, 7, 10, 1, 3, 1, 8, 6, 5, 6, 2, 1, 5, 8, 6, 1, 11, 1, 12, 3, 7, 1, 6, 4, 7, 8, 10, 1, 9, 10, 16, 10, 9, 1, 8, 1, 5, 13, 10, 12, 15, 1, 12, 10, 7, 1, 8, 1, 7, 5, 10, 8, 11, 1, 12, 6, 9, 1, 8, 10, 9, 12, 14, 1, 9, 10, 12, 10, 7, 12, 6, 1, 13, 17, 14, 1, 11, 1, 14, 9

Offset

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base

Formula

a(n) = A276150(A328769(n)).

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A328769(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i, 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); };
A328772(n) = A276150(A328769(n));

Crossrefs

Cf. A002110, A276150, A324888, A328769, A328771.

Sequence in context: A316211 A329480 A277895 * A300726 A325352 A305438

Adjacent sequences: A328769 A328770 A328771 * A328773 A328774 A328775

Keyword

nonn

Author

Antti Karttunen, Oct 28 2019

Status

approved