

A069281


20almost primes (generalization of semiprimes).


31



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

1,1


COMMENTS

Product of 20 not necessarily distinct primes.
Divisible by exactly 20 prime powers (not including 1).
Any 20almost prime can be represented in several ways as a product of two 10almost primes A046314; in several ways as a product of four 5almost primes A014614; in several ways as a product of five 4almost 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.
a(n) = A078840(20,n).  R. J. Mathar, Jan 30 2019


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 bruteforce method above may be desirable. See additional comments in this section of A069280.


CROSSREFS

Cf. A101637, A101638, A101605, A101606.
Sequences listing ralmost 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



