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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 &] (* 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 December 12 19:33 EST 2018. Contains 318081 sequences. (Running on oeis4.)