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A046310 Numbers that are divisible by exactly 8 primes counting multiplicity. 51
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
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).
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
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)