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A324341 If 2n = 2^e1 + ... + 2^ek [e1 .. ek distinct], then a(n) is the number of nonzero digits when A002110(e1) * ... * A002110(ek) is written in primorial base.

%I A324341 #13 Feb 24 2019 01:59:51
%S A324341 1,1,1,1,1,1,1,2,1,1,1,2,2,2,3,3,1,1,1,1,2,2,2,3,2,3,3,3,4,2,2,3,1,1,
%T A324341 1,1,2,2,2,3,2,3,3,3,3,3,3,4,3,3,4,4,4,4,5,5,5,5,5,4,6,6,6,6,1,1,1,1,
%U A324341 2,2,2,2,2,2,3,3,3,3,4,4,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,4,4,4,4,5,5,5,5,5,5
%N A324341 If 2n = 2^e1 + ... + 2^ek [e1 .. ek distinct], then a(n) is the number of nonzero digits when A002110(e1) * ... * A002110(ek) is written in primorial base.
%C A324341 Number of nonzero digits when A283477(n) is represented in primorial base, A049345.
%C A324341 Number of distinct prime factors in A324289(n).
%H A324341 Antti Karttunen, <a href="/A324341/b324341.txt">Table of n, a(n) for n = 0..16384</a>
%H A324341 Antti Karttunen, <a href="/A324341/a324341.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A324341 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324341 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A324341 a(n) = A267263(A283477(n)).
%F A324341 a(n) = A001221(A324289(n)) = A001221(A276086(A283477(n))).
%F A324341 a(n) <= A324342(n).
%o A324341 (PARI)
%o A324341 A002110(n) = prod(i=1,n,prime(i));
%o A324341 A030308(n,k) = bittest(n,k);
%o A324341 A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
%o A324341 A267263(n) = { my(s=0); forprime(p=2, , if(n%p, s++, if(n==0, return(s))); n\=p); }; \\ From A267263
%o A324341 A324341(n) = A267263(A283477(n));
%Y A324341 Cf. A001221, A002110, A049345, A267263, A276086, A283477, A324289, A324342.
%K A324341 nonn
%O A324341 0,8
%A A324341 _Antti Karttunen_, Feb 23 2019