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A046312 Numbers that are divisible by exactly 9 primes with multiplicity. 37
512, 768, 1152, 1280, 1728, 1792, 1920, 2592, 2688, 2816, 2880, 3200, 3328, 3888, 4032, 4224, 4320, 4352, 4480, 4800, 4864, 4992, 5832, 5888, 6048, 6272, 6336, 6480, 6528, 6720, 7040, 7200, 7296, 7424, 7488, 7936, 8000, 8320, 8748, 8832, 9072, 9408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called 9-almost primes. Products of exactly 9 primes (not necessarily distinct). - Jonathan Vos Post, Dec 11 2004

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Reference

FORMULA

Product p_i^e_i with Sum e_i = 9.

a(n) ~ 40320n log n / (log log n)^8. - Charles R Greathouse IV, May 06 2013

MATHEMATICA

Select[Range[2200], Plus @@ Last /@ FactorInteger[ # ] == 9 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)

PROG

(PARI) is(n)=bigomega(n)==9 \\ Charles R Greathouse IV, Mar 21 2013

CROSSREFS

Cf. A046311, A120050 (number of 9-almost primes <= 10^n).

Cf. A101637, A101638, A101605, A101606.

Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), this sequence (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20). - Jason Kimberley, Oct 02 2011

Sequence in context: A202461 A046311 A036333 * A045033 A066648 A043423

Adjacent sequences:  A046309 A046310 A046311 * A046313 A046314 A046315

KEYWORD

nonn

AUTHOR

Patrick De Geest, Jun 15 1998

STATUS

approved

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Last modified December 7 23:08 EST 2016. Contains 278900 sequences.