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.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Feb 23 2019

Keywords

• nonn

Comments

Number of nonzero digits when A283477(n) is represented in primorial base, A049345.

Number of distinct prime factors in A324289(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A001221, A002110, A049345, A267263, A276086, A283477, A324289, A324342.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A030308(n,k) = bittest(n,k);
A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
A267263(n) = { my(s=0); forprime(p=2, , if(n%p, s++, if(n==0, return(s))); n\=p); }; \\ From A267263
A324341(n) = A267263(A283477(n));

Formula

a(n) = A267263(A283477(n)).

a(n) = A001221(A324289(n)) = A001221(A276086(A283477(n))).

a(n) <= A324342(n).