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

0,8

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

Formula

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

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

a(n) <= A324342(n).

Prog

(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));

Crossrefs

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

Sequence in context: A299825 A362756 A289493 * A271325 A228431 A328702

Adjacent sequences: A324338 A324339 A324340 * A324342 A324343 A324344

Keyword

nonn

Author

Antti Karttunen, Feb 23 2019

Status

approved