%I #19 Feb 24 2019 01:59:59
%S 1,1,1,2,1,2,6,6,1,2,6,2,10,10,8,16,1,2,6,12,6,12,24,20,18,20,28,28,
%T 26,6,18,24,1,2,6,12,14,12,20,6,18,18,22,26,38,20,16,16,24,32,42,44,
%U 34,50,68,70,36,54,60,54,70,56,60,82,1,2,6,12,12,6,18,36,12,24,28,34,34,50,50,72,22,26,28,34,38,54,40,52,28,38,56
%N If 2n = 2^e1 + ... + 2^ek [e1 .. ek distinct], then a(n) is the minimal number of primorials (A002110) that add to A002110(e1) * ... * A002110(ek).
%C When A283477(n) is written in primorial base (A049345), then a(n) is the sum of digits (with unlimited digit values), thus also the minimal number of primorials (A002110) that add to A283477(n).
%C Number of prime factors in A324289(n), counted with multiplicity.
%C Each subsequence starting at each n = 2^k is converging towards A283477: 1, 2, 6, 12, 30, 60, 180, 360, 210, 420, etc. See also comments in A324289.
%H Antti Karttunen, <a href="/A324342/b324342.txt">Table of n, a(n) for n = 0..16384</a>
%H Antti Karttunen, <a href="/A324342/a324342.txt">Data supplement: n, a(n) computed for n = 0..65555</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(n) = A276150(A283477(n)).
%F a(n) = A001222(A324289(n)) = A001222(A276086(A283477(n))).
%F a(n) >= A324341(n).
%F a(2^n) = 1 for all n >= 0.
%o (PARI)
%o A002110(n) = prod(i=1,n,prime(i));
%o A030308(n,k) = bittest(n,k);
%o A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
%o A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
%o A324342(n) = A276150(A283477(n));
%Y Cf. A001222, A002110, A049345, A276086, A276150, A283477, A324289, A324341.
%K nonn
%O 0,4
%A _Antti Karttunen_, Feb 23 2019