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A046314
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Numbers that are divisible by exactly 10 primes with multiplicity.
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45
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Reference
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(n)=bigomega(n)==10 \\ Charles R Greathouse IV, Mar 21 2013
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest, Jun 15 1998
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STATUS
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approved
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