A329040 Number of distinct primorials in the greedy sum of primorials adding to A108951(n).

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 3, 2, 3, 1, 1, 1, 1, 3

Offset: 1

Author

Antti Karttunen, Nov 11 2019

Keywords

• nonn

Comments

The greedy sum is also the sum with the minimal number of primorials used in the primorial base representation.

Examples

			For n = 18 = 2 * 3^2, A108951(18) = A034386(2) * A034386(3)^2 = 2 * 6^2 = 72 = 2*A002110(3) + 2*A002110(2) = 2*30 + 2*6, and because there occurs only two distinct primorials (30 and 6) in the sum, we have a(18) = 2.
		

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
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001221, A002110, A034386, A108951, A267263, A276086, A324886, A324888, A329051 (positions of records), A329343.

Cf. also A329045, A329046.

Programs

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324886(n) = A276086(A108951(n));
A329040(n) = omega(A324886(n));

Formula

a(n) = A001221(A324886(n)).

a(n) = A267263(A108951(n)).

a(n) <= A324888(n).