Search: id:A014612
Results 1-1 of 1 results found.

%I A014612
%S A014612 8,12,18,20,27,28,30,42,44,45,50,52,63,66,68,70,75,76,78,92,98,99,102,
%T A014612 105,110,114,116,117,124,125,130,138,147,148,153,154,164,165,170,171,
%U A014612 172,174,175,182,186,188,190,195,207,212,222,230,231,236,238,242,244
%N A014612 Numbers that are divisible by exactly 3 primes (counted with multiplicity).
%C A014612 Sometimes called "triprimes" or "3-almost primes".
%C A014612 See also A001358 for product of two primes (sometimes called semiprimes).
%C A014612 If you graph a(n)/n for n up to 10000 (and probably quite a bit higher), 
               it appears to be converging to something near 3.9. In fact the limit 
               is infinite. - Franklin T. Adams-Watters, Sep 20 2006
%C A014612 Even the first 10K terms look fairly linear; even after subtracting out 
               the linear portion the plot looks fairly straight, although perhaps 
               the variation is increasing with n. - Richard A. Becker, Oct 02 2006
%C A014612 Meng proved that for any sufficiently large odd integer n, the equation 
               n = a + b + c has solutions where each of a, b, c are 3-almost primes 
               (A014612). The number of such solutions, where lg x = log (base 2)(x), 
               is (1/2)((((lg n)/log n))^2)/(2 log n))^(1/3))(sigma(n))(n^2)(1+O(1/
               lg n)) where sigma(n) is a convergent series given by Meng which 
               is > (1/2). - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 16 
               2005
%C A014612 Or, composite numbers with equal count of nontrivial prime divisors and 
               nontrivial nonprime divisors. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Nov 02 2009]
%D A014612 E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Vol. 
               1, Teubner, Leipzig; third edition : Chelsea, New York (1974).
%D A014612 Xianmeng Meng, On sums of three integers with a fixed number of prime 
               factors, Journal of Number Theory, Vol. 114 (2005), pp. 37-65.
%H A014612 T. D. Noe, <a href="b014612.txt">Table of n, a(n) for n=1..10000</a>
%H A014612 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlmostPrime.html">Link to a section of The World of Mathematics.</
               a>
%F A014612 Product p_i^e_i with Sum e_i = 3.
%F A014612 a(n) ~ 2n log n / (log log n)^2 as n -> infinity [Landau, p. 211].
%t A014612 fQ[n_] := Plus @@ Last /@ FactorInteger@n == 3; Select[ Range@244, fQ[ 
               # ] &] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 04 2006)
%t A014612 Select[Range[160], Plus @@ Last /@ FactorInteger[ # ] == 3 &] - Vladimir 
               Orlovsky, Apr 23 2008
%Y A014612 Cf. A000040, A001358 (biprimes), A014613 (quadruprimes), A033942, A086062, 
               A098238, A123072, A123073.
%Y A014612 Cf. A109251 (number of 3-almost primes <= 10^n).
%Y A014612 Subsequence of A145784. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 19 2008]
%Y A014612 Sequence in context: A067537 A046339 A145784 this_sequence A046369 A066428 
               A054397
%Y A014612 Adjacent sequences: A014609 A014610 A014611 this_sequence A014613 A014614 
               A014615
%K A014612 nonn
%O A014612 1,1
%A A014612 Eric Weisstein (eric(AT)weisstein.com)
%E A014612 More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 
               1998.

Search completed in 0.003 seconds