A376420 a(n) is the next number after n! with the same number of prime factors as n!, counted with multiplicity.

3, 9, 36, 162, 800, 5248, 41984, 364544, 3639168, 39937536, 479250432, 6227066880, 87178936320, 1307674935296, 20922798964736, 355687506903040

Offset

2,1

Links

Table of n, a(n) for n=2..17.

Formula

A001222(a(n)) = A022559(n).

a(n+1) <= (n+1) * a(n), with equality for n = 2, 3, 7, 11, 13, 15, ...

Example

a(4) = 36 because 4! = 24 = 2^3 * 3 and 36 = 2^2 * 3^2 both have 4 prime factors, counted with multiplicity, and no numbers between 24 and 36 have exactly 4 prime factors.

Maple

f:= proc(n) local x, t;
 t:= numtheory:-bigomega(n);
 for x from n!+1 do
   if numtheory:-bigomega(x) = t then return x fi
 od
end proc:
map(f, [$2..16]);

Mathematica

s={}; Do[i=n!+1; ponf=PrimeOmega[n!]; While[!ponf==PrimeOmega[i], i++]; AppendTo[s, i] , {n, 2, 14}]; s (* James C. McMahon, Sep 23 2024 *)

Crossrefs

Cf. A000142, A001222, A022559.

Sequence in context: A394959 A295739 A156016 * A032314 A144352 A107895

Adjacent sequences: A376417 A376418 A376419 * A376421 A376422 A376423

Keyword

nonn

Author

Robert Israel, Sep 22 2024

Status

approved