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A069273 12-almost primes (generalization of semiprimes). 32
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 at least one way as a product of two 6-almost primes A046306, three 4-almost primes A014613, four 3-almost primes A014612, or 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 *)

Select[Range[60000], PrimeOmega[#]==12&] (* Harvey P. Dale, May 01 2019 *)

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 A258735

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 October 29 18:53 EDT 2020. Contains 338067 sequences. (Running on oeis4.)