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

1,8

Comments

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

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

Formula

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

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

a(n) <= A324888(n).

Example

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.

Prog

(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));

Crossrefs

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

Cf. also A329045, A329046.

Sequence in context: A172299 A025453 A094215 * A296978 A236000 A114139

Adjacent sequences: A329037 A329038 A329039 * A329041 A329042 A329043

Keyword

nonn

Author

Antti Karttunen, Nov 11 2019

Status

approved