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A365461 Sum of digits when A181821(n) is written in primorial base (A049345).

%I A365461 #9 Sep 15 2023 18:53:29
%S A365461 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 A365461 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 A365461 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 A365461 Sum of digits when A181821(n) is written in primorial base (A049345).
%C A365461 Minimal number of primorials (A002110) that add to A181821(n).
%H A365461 Antti Karttunen, <a href="/A365461/b365461.txt">Table of n, a(n) for n = 1..65537</a>
%H A365461 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A365461 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A365461 a(n) = A276150(A181821(n)).
%F A365461 a(n) = A324888(A122111(n)).
%F A365461 a(n) >= A365460(n).
%o A365461 (PARI)
%o A365461 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 A365461 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 A365461(n) = A276150(A181821(n));
%Y A365461 Cf. A002110, A049345, A122111, A181821, A276150, A324888, A365460.
%K A365461 nonn
%O A365461 1,3
%A A365461 _Antti Karttunen_, Sep 15 2023