

A046310


Numbers that are divisible by exactly 8 primes counting multiplicity.


47



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

1,1


COMMENTS

Also called 8almost primes. Products of exactly 8 primes (not necessarily distinct). Any 8almost prime can be represented in several ways as a product of two 4almost 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


MAPLE

A046310 := proc(n)
option remember;
if n = 1 then
2^8 ;
else
for a from procname(n1)+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 8almost primes <= 10^n).
Cf. A101637, A101638, A101605, A101606.
Sequences listing ralmost 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



