

A046314


Numbers that are divisible by exactly 10 primes with multiplicity.


42



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

1,1


COMMENTS

Also called 10almost primes. Products of exactly 10 primes (not necessarily distinct). Any 10almost prime can be represented in several ways as a product of two 5almost 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 10almost 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), 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



