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A069273 12-almost primes (generalization of semiprimes). 32

%I #29 May 06 2019 12:10:34

%S 4096,6144,9216,10240,13824,14336,15360,20736,21504,22528,23040,25600,

%T 26624,31104,32256,33792,34560,34816,35840,38400,38912,39936,46656,

%U 47104,48384,50176,50688,51840,52224,53760,56320,57600,58368,59392

%N 12-almost primes (generalization of semiprimes).

%C Product of 12 not necessarily distinct primes.

%C Divisible by exactly 12 prime powers (not including 1).

%C 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

%H D. W. Wilson, <a href="/A069273/b069273.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime.</a>

%F Product p_i^e_i with Sum e_i = 12.

%t Select[Range[20000], Plus @@ Last /@ FactorInteger[ # ] == 12 &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2008 *)

%t Select[Range[60000],PrimeOmega[#]==12&] (* _Harvey P. Dale_, May 01 2019 *)

%o (PARI) k=12; start=2^k; finish=70000; v=[] for(n=start,finish, if(bigomega(n)==k,v=concat(v,n))); v

%Y Cf. A101637, A101638, A101605, A101606.

%Y 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

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Mar 13 2002

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Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)