A365461 - OEIS

%I #9 Sep 15 2023 18:53:29

%S 1,1,2,1,2,2,4,1,2,4,2,2,4,4,4,1,6,6,6,4,8,4,6,2,2,8,6,2,12,6,16,1,6,

%T 10,4,6,16,10,8,4,10,6,10,4,12,10,6,2,8,6,10,8,12,10,8,8,20,10,18,2,

%U 26,14,8,1,12,12,22,10,20,12,28,6,28,14,10,10,6,8,34,4,8,18,38,4,10,14,20,6,52,10,12,10,24

%N Sum of digits when A181821(n) is written in primorial base (A049345).

%C Minimal number of primorials (A002110) that add to A181821(n).

%H Antti Karttunen, <a href="/A365461/b365461.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) = A276150(A181821(n)).

%F a(n) = A324888(A122111(n)).

%F a(n) >= A365460(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 A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };

%o A365461(n) = A276150(A181821(n));

%Y Cf. A002110, A049345, A122111, A181821, A276150, A324888, A365460.

%K nonn

%O 1,3

%A _Antti Karttunen_, Sep 15 2023