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A069276 15-almost primes (generalization of semiprimes). 29

%I #24 Aug 14 2019 15:22:08

%S 32768,49152,73728,81920,110592,114688,122880,165888,172032,180224,

%T 184320,204800,212992,248832,258048,270336,276480,278528,286720,

%U 307200,311296,319488,373248,376832,387072,401408,405504,414720,417792,430080

%N 15-almost primes (generalization of semiprimes).

%C Product of 15 not necessarily distinct primes.

%C Divisible by exactly 15 prime powers (not including 1).

%C Any 15-almost prime can be represented in several ways as a product of three 5-almost primes A014614, and in several ways as a product of five 3-almost primes A014612. - _Jonathan Vos Post_, Dec 11 2004

%H D. W. Wilson, <a href="/A069276/b069276.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 = 15.

%t Select[Range[90000], Plus @@ Last /@ FactorInteger[ # ] == 15 &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2008 *)

%t Select[Range[450000],PrimeOmega[#]==15&] (* _Harvey P. Dale_, Aug 14 2019 *)

%o (PARI) k=15; start=2^k; finish=500000; 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), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), this sequence (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 March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)