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

0,4

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

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.

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)));
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));

Crossrefs

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

Sequence in context: A061569 A294523 A286651 * A140835 A300350 A300435

Adjacent sequences: A324339 A324340 A324341 * A324343 A324344 A324345

Keyword

nonn

Author

Antti Karttunen, Feb 23 2019

Status

approved