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A069273 12-almost 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Product of 12 not necessarily distinct primes.

Divisible by exactly 12 prime powers (not including 1).

Any 12-almost prime can be represented in several ways as a product of two 6-almost primes A046306; in several ways as a product of three 4-almost primes A014613; in several ways as a product of four 3-almost 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 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), 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

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Last modified December 22 21:10 EST 2014. Contains 252372 sequences.