A118476 a(0) = 1; a(n) is least k with n prime factors and k > n*a(n-1).

1, 2, 6, 20, 81, 408, 2480, 17376, 139040, 1251450, 12514816, 137663064, 1651956992, 21475443200, 300656206080, 4509843098112, 72157489576704, 1226677322842112, 22080191811166208, 419523644412176256, 8390472888243683328, 176199930653117513728

Offset: 0

Author

Jonathan Vos Post, May 04 2006

Keywords

• easy
• nonn

Comments

This is a super-polynomial function, as for positive n, a(n) > n!.

Prime factors counted with multiplicity. - Harvey P. Dale, Aug 25 2019

Examples

			a(1) = 2 because 2 is the smallest prime (integer with 1 prime factor) greater than 1 * 1 = 1.
a(2) = 6 because 6 = 2 * 3 is the smallest semiprime (integer with 2 prime factors) greater than 2 * 2 = 4.
a(3) = 20 because 20 = 2^2*5 is the smallest 3-almost prime (integer with 3 prime factors) greater than 3 * 6 = 18.
		

Links

• Eric Weisstein's World of Mathematics, Almost Prime.

Crossrefs

Cf. A000040, A001358, A055496, A076656.

Programs

Maple

A118476 := proc(n) option remember; local k; if n = 0 then 1; else for k from n*procname(n-1)+1 do if numtheory[bigomega](k) = n then return k; end if; end do: end if; end proc:
seq(A118476(n),n=0..14) ; # R. J. Mathar, Dec 22 2010

Mathematica

lkpf[{n_,a_}]:=Module[{k=a(n+1)+1},While[PrimeOmega[k]!=n+1,k++];{n+1,k}]; NestList[lkpf,{0,1},21][[All,2]] (* Harvey P. Dale, Aug 25 2019 *)

Formula

a(0) = 1; a(n) least n-almost prime > n*a(n-1).

Extensions

Terms corrected from a(4) on by R. J. Mathar, Dec 22 2010

a(15)-a(21) from Donovan Johnson, Jan 06 2011