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A046310 Numbers that are divisible by exactly 8 primes counting multiplicity. 40
256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4160, 4374, 4416, 4536, 4704, 4736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called 8-almost primes. Products of exactly 8 primes (not necessarily distinct). Any 8-almost prime can be represented in several ways as a product of two 4-almost primes A014613 and in several ways as a product of four semiprimes A001358. - 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 = 8.

a(n) ~ 5040n log n / (log log n)^7. - Charles R Greathouse IV, May 06 2013

MATHEMATICA

Select[Range[1600], Plus @@ Last /@ FactorInteger[ # ] == 8 &] - Vladimir Orlovsky, Apr 23 2008

Select[Range[5000], PrimeOmega[#]==8&]  (* Harvey P. Dale, Apr 19 2011 *)

PROG

(PARI) is(n)=bigomega(n)==8 \\ Charles R Greathouse IV, Mar 21 2013

CROSSREFS

Cf. A046309, A120049 (number of 8-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), this sequence (r = 8), A046312 (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: A046309 A036332 A114987 * A115176 A221259 A223693

Adjacent sequences:  A046307 A046308 A046309 * A046311 A046312 A046313

KEYWORD

nonn

AUTHOR

Patrick De Geest, Jun 15 1998.

STATUS

approved

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Last modified September 2 20:37 EDT 2014. Contains 246367 sequences.