

A118476


a(0) = 1; a(n) is least k with n prime factors and k > n*a(n1).


1



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

0,2


COMMENTS

This is a superpolynomial function, as for positive n, a(n) > n!.
Prime factors counted with multiplicity.  Harvey P. Dale, Aug 25 2019


LINKS

Table of n, a(n) for n=0..21.
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

a(0) = 1; a(n) least nalmost prime > n*a(n1).


EXAMPLE

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 3almost prime (integer with 3 prime factors) greater than 3 * 6 = 18.


MAPLE

A118476 := proc(n) option remember; local k; if n = 0 then 1; else for k from n*procname(n1)+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 *)


CROSSREFS

Cf. A000040, A001358, A055496, A076656.
Sequence in context: A117574 A177481 A177475 * A260788 A337274 A115084
Adjacent sequences: A118473 A118474 A118475 * A118477 A118478 A118479


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, May 04 2006


EXTENSIONS

Terms corrected from a(4) on by R. J. Mathar, Dec 22 2010
a(15)a(21) from Donovan Johnson, Jan 06 2011


STATUS

approved



