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A046310
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Numbers that are divisible by exactly 8 primes counting multiplicity.
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40
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Reference
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FORMULA
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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
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MATHEMATICA
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Select[Range[1600], Plus @@ Last /@ FactorInteger[ # ] == 8 &] - Vladimir Orlovsky, Apr 23 2008
Select[Range[5000], PrimeOmega[#]==8&] (* From Harvey P. Dale, Apr 19 2011 *)
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PROG
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(PARI) is(n)=bigomega(n)==8 \\ Charles R Greathouse IV, Mar 21 2013
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest, Jun 15 1998.
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STATUS
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approved
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