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A069281 20-almost primes (generalization of semiprimes). 30
1048576, 1572864, 2359296, 2621440, 3538944, 3670016, 3932160, 5308416, 5505024, 5767168, 5898240, 6553600, 6815744, 7962624, 8257536, 8650752, 8847360, 8912896, 9175040, 9830400, 9961472, 10223616, 11943936, 12058624 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Product of 20 not necessarily distinct primes.

Divisible by exactly 20 prime powers (not including 1).

Any 20-almost prime can be represented in several ways as a product of two 10-almost primes A046314; in several ways as a product of four 5-almost primes A014614; in several ways as a product of five 4-almost primes A014613; and in several ways as a product of ten semiprimes A001358. - Jonathan Vos Post, Dec 12 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 = 20.

MATHEMATICA

Select[Range[2*9!, 5*10! ], Plus@@Last/@FactorInteger[ # ]==20 &] [From Vladimir Joseph Stephan Orlovsky, Feb 26 2009]

PROG

(PARI) k=20; start=2^k; finish=15000000; v=[] for(n=start, finish, if(bigomega(n)==k, v=concat(v, n))); v Depending upon the size of k and how many terms are needed, a much more efficient algorithm than the brute-force method above may be desirable. See additional comments in this section of A069280.

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), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19),  this sequence (r = 20). - Jason Kimberley, Oct 02 2011

Sequence in context: A069395 A223603 A223696 * A224804 A016786 A016810

Adjacent sequences:  A069278 A069279 A069280 * A069282 A069283 A069284

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Mar 13 2002

STATUS

approved

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Last modified September 1 14:28 EDT 2014. Contains 246307 sequences.