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A046314 Numbers that are divisible by exactly 10 primes with multiplicity. 40
1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728, 9984, 11664, 11776, 12096, 12544, 12672, 12960, 13056, 13440, 14080, 14400, 14592, 14848, 14976, 15872, 16000, 16640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called 10-almost primes. Products of exactly 10 primes (not necessarily distinct). Any 10-almost prime can be represented in several ways as a product of two 5-almost primes A014614 and in several ways as a product of five semiprimes A001358. - Jonathan Vos Post, Dec 11 2004

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 = 10.

a(n) ~ 362880n log n / (log log n)^9. - Charles R Greathouse IV, May 06 2013

MATHEMATICA

Select[Range[5000], Plus @@ Last /@ FactorInteger[ # ] == 10 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)

Select[Range[17000], PrimeOmega[#]==10&] (* Harvey P. Dale, Jun 23 2018 *)

PROG

(PARI) is(n)=bigomega(n)==10 \\ Charles R Greathouse IV, Mar 21 2013

CROSSREFS

Cf. A046313, A120051 (number of 10-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), A046310 (r = 8), A046312 (r = 9), this sequence (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: A074211 A057443 A046313 * A221260 A223065 A298607

Adjacent sequences:  A046311 A046312 A046313 * A046315 A046316 A046317

KEYWORD

nonn

AUTHOR

Patrick De Geest, Jun 15 1998

STATUS

approved

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Last modified December 12 19:33 EST 2018. Contains 318081 sequences. (Running on oeis4.)