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A046310 Numbers that are divisible by exactly 8 primes counting multiplicity. 44
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

Odd terms are in A046321; first odd term is a(64)=6561=3^8. - Zak Seidov, Feb 08 2016

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 Joseph Stephan 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).

Cf. A046321.

Sequence in context: A046309 A036332 A114987 * A115176 A299156 A221259

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 December 14 21:09 EST 2018. Contains 318132 sequences. (Running on oeis4.)