

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
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OFFSET

1,1


COMMENTS

Also called 9almost 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 9almost primes <= 10^n).
Cf. A101637, A101638, A101605, A101606.
Sequences listing ralmost 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



