A324342 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).

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, 26, 6, 18, 24, 1, 2, 6, 12, 14, 12, 20, 6, 18, 18, 22, 26, 38, 20, 16, 16, 24, 32, 42, 44, 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

Offset: 0

Author

Antti Karttunen, Feb 23 2019

Keywords

• nonn

Comments

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).

Number of prime factors in A324289(n), counted with multiplicity.

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65555
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001222, A002110, A049345, A276086, A276150, A283477, A324289, A324341.

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)));
A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
A324342(n) = A276150(A283477(n));

Formula

a(n) = A276150(A283477(n)).

a(n) = A001222(A324289(n)) = A001222(A276086(A283477(n))).

a(n) >= A324341(n).

a(2^n) = 1 for all n >= 0.