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 A046310 Numbers that are divisible by exactly 8 primes counting multiplicity. 50
 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 a(n) = A078840(8,n). - R. J. Mathar, Jan 30 2019 MAPLE A046310 := proc(n)     option remember;     if n = 1 then         2^8 ;     else         for a from procname(n-1)+1 do             if numtheory[bigomega](a) = 8 then                 return a;             end if;         end do:     end if; end proc: seq(A046310(n), n=1..30) ; # R. J. Mathar, Dec 21 2018 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 June 24 04:50 EDT 2021. Contains 345416 sequences. (Running on oeis4.)