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A046312 Numbers that are divisible by exactly 9 primes with multiplicity. 45
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
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 *)
Select[Range[10000], PrimeOmega[#]==9&] (* Harvey P. Dale, Oct 24 2020 *)
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).
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
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)