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A069281
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20-almost primes (generalization of semiprimes).
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32
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1048576, 1572864, 2359296, 2621440, 3538944, 3670016, 3932160, 5308416, 5505024, 5767168, 5898240, 6553600, 6815744, 7962624, 8257536, 8650752, 8847360, 8912896, 9175040, 9830400, 9961472, 10223616, 11943936, 12058624
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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D. W. Wilson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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Product p_i^e_i with Sum e_i = 20.
a(n) = A078840(20,n). - R. J. Mathar, Jan 30 2019
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MATHEMATICA
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Select[Range[2*9!, 5*10! ], Plus@@Last/@FactorInteger[ # ]==20 &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
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PROG
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(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.
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd, Mar 13 2002
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STATUS
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approved
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