A365460 - OEIS

%I #9 Sep 15 2023 18:53:25

%S 1,1,1,1,2,1,2,1,2,1,2,1,2,2,2,1,3,1,4,1,2,2,3,1,2,2,2,2,3,2,4,1,3,3,

%T 2,1,5,3,3,1,3,2,3,2,2,3,5,1,3,2,3,2,5,2,2,1,3,4,5,2,5,4,3,1,3,2,6,2,

%U 4,2,6,1,6,4,3,3,4,3,6,1,3,3,7,2,4,4,4,2,8,2,4,3,4,4,4,1,6,3,3,2,6,3,7,2,3

%N Number of distinct primorials in the greedy sum of primorials adding to A181821(n).

%H Antti Karttunen, <a href="/A365460/b365460.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A267263(A181821(n)).

%F a(n) = A329040(A122111(n)).

%F a(n) <= A365461(n).

%o (PARI)

%o A181821(n) = { my(f=factor(n),p=0,m=1); forstep(i=#f~,1,-1,while(f[i,2], f[i,2]--; m *= (p=nextprime(p+1))^primepi(f[i,1]))); (m); };

%o A267263(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += !!d; n = (n-d)/p; p = nextprime(1+p)); (s); };

%o A365460(n) = A267263(A181821(n));

%Y Cf. A122111, A181821, A267263, A329040.

%Y Cf. also A365461.

%K nonn

%O 1,5

%A _Antti Karttunen_, Sep 15 2023