

A069273


12almost primes (generalization of semiprimes).


30



4096, 6144, 9216, 10240, 13824, 14336, 15360, 20736, 21504, 22528, 23040, 25600, 26624, 31104, 32256, 33792, 34560, 34816, 35840, 38400, 38912, 39936, 46656, 47104, 48384, 50176, 50688, 51840, 52224, 53760, 56320, 57600, 58368, 59392
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OFFSET

1,1


COMMENTS

Product of 12 not necessarily distinct primes.
Divisible by exactly 12 prime powers (not including 1).
Any 12almost prime can be represented in several ways as a product of two 6almost primes A046306; in several ways as a product of three 4almost primes A014613; in several ways as a product of four 3almost primes A014612; and in several ways as a product of six semiprimes A001358.  Jonathan Vos Post, Dec 11 2004


LINKS

D. W. Wilson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

Product p_i^e_i with Sum e_i = 12.


MATHEMATICA

Select[Range[20000], Plus @@ Last /@ FactorInteger[ # ] == 12 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)


PROG

(PARI) k=12; start=2^k; finish=70000; v=[] for(n=start, finish, if(bigomega(n)==k, v=concat(v, n))); v


CROSSREFS

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), A046314 (r = 10), A069272 (r = 11), this sequence (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: A223694 A186489 A221261 * A043424 A138174 A180972
Adjacent sequences: A069270 A069271 A069272 * A069274 A069275 A069276


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Mar 13 2002


STATUS

approved



