cp's OEIS Frontend

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

%I A329040 #14 Nov 11 2019 18:43:02
%S A329040 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,
%T A329040 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,
%U A329040 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
%N A329040 Number of distinct primorials in the greedy sum of primorials adding to A108951(n).
%C A329040 The greedy sum is also the sum with the minimal number of primorials used in the primorial base representation.
%H A329040 Antti Karttunen, <a href="/A329040/b329040.txt">Table of n, a(n) for n = 1..65537</a>
%H A329040 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329040 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A329040 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A329040 a(n) = A001221(A324886(n)).
%F A329040 a(n) = A267263(A108951(n)).
%F A329040 a(n) <= A324888(n).
%e A329040 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.
%o A329040 (PARI)
%o A329040 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329040 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329040 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329040 A324886(n) = A276086(A108951(n));
%o A329040 A329040(n) = omega(A324886(n));
%Y A329040 Cf. A001221, A002110, A034386, A108951, A267263, A276086, A324886, A324888, A329051 (positions of records), A329343.
%Y A329040 Cf. also A329045, A329046.
%K A329040 nonn
%O A329040 1,8
%A A329040 _Antti Karttunen_, Nov 11 2019