|
| |
|
|
A118476
|
|
a(0) = 1; a(n) is least k with n prime factors and k > n*a(n-1).
|
|
1
| |
|
|
1, 2, 6, 20, 81, 408, 2480, 17376, 139040, 1251450, 12514816, 137663064, 1651956992, 21475443200, 300656206080, 4509843098112, 72157489576704, 1226677322842112, 22080191811166208, 419523644412176256, 8390472888243683328, 176199930653117513728
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| This is a super-polynomial function, as for positive n, a(n) > n!.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Almost Prime.
|
|
|
FORMULA
| a(0) = 1; a(n) least n-almost prime > n*a(n-1).
|
|
|
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 3-almost 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(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
|
|
|
CROSSREFS
| Cf. A000040, A001358, A055496, A076656.
Sequence in context: A117574 A177481 A177475 * A115084 A177476 A177474
Adjacent sequences: A118473 A118474 A118475 * A118477 A118478 A118479
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 04 2006
|
|
|
EXTENSIONS
| Terms corrected from a(4) on - R. J. Mathar, Dec 22 2010
a(15)-a(21) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 06 2011
|
| |
|
|
