Search: id:A006881
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%I A006881 M4082
%S A006881 6,10,14,15,21,22,26,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,82,85,
%T A006881 86,87,91,93,94,95,106,111,115,118,119,122,123,129,133,134,141,142,143,
%U A006881 145,146,155,158,159,161,166,177,178,183,185,187,194,201,202,203,205
%N A006881 Numbers that are the product of two distinct primes.
%C A006881 Numbers n such that phi(n)+sigma(n)=2*(n+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Mar 02 2002
%C A006881 n such that tau(n)=omega(n)^omega(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Sep 10 2002
%C A006881 Could also be called square-free semiprimes (or 2-almost primes). - Rick 
               L. Shepherd (rshepherd2(AT)hotmail.com), May 11 2003
%C A006881 Goldston et al. proved that lim inf [as n approaches infinity] (a(n+1) 
               - a(n)) =< 26. If an appropriate generalization of the Elliott-Halberstam 
               Conjecture is true, then the above bound can be improved to 6. - 
               Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 20 2005
%C A006881 A000005(a(n)^(k-1)) = A000290(k) for all k>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 04 2007
%C A006881 The maximal number of consecutive integers in this sequence is 3 - there 
               can not be 4 consecutive integers because one of them would be divisible 
               by 4 and therefore would not be product of distinct primes. There 
               are several examples of 3 consecutive integers in this sequence. 
               The first one is 33=3.11, 34=2.17, 35=5.7. - Matias Saucedo (solomatias(AT)yahoo.com.ar), 
               Mar 15 2008
%D A006881 D. A. Goldston, S. W. Graham, J. Pimtz and Y. Yildirim, "Small Gaps Between 
               Primes or Almost Primes", arXiv:math.NT/0506067 v1, 3 2005.
%D A006881 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006881 T. D. Noe, <a href="b006881.txt">Table of n, a(n) for n=1..10000</a>
%H A006881 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Semiprime.html">Semiprime</a>
%F A006881 A002033(a(n))=3. - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 
               26 2009
%t A006881 Take[ Sort@ Flatten@ Table[Prime[m]*Prime[n], {n, 2, 26}, {m, n - 1}], 
               60] (Robert G. Wilson v (rgwv(at)rgwv.com), Dec 28 2005)
%o A006881 (PARI) for(n=1,214,if(bigomega(n)==2&&omega(n)==2,print1(n,","))) for(n=1,
               214,if(bigomega(n)==2&&issquarefree(n),print1(n,",")))
%Y A006881 Cf. A046386, A046387, A067885 (product of 4, 5 and 6 distinct primes, 
               resp.)
%Y A006881 Cf. A030229, A051709.
%Y A006881 Cf. A001221 (omega(n)), A001222 (bigomega(n)), A001358 (semiprimes), 
               A005117 (square-free), A007304 (square-free 3-almost primes).
%Y A006881 Sequence in context: A000469 A120944 A052053 this_sequence A030229 A162730 
               A093772
%Y A006881 Adjacent sequences: A006878 A006879 A006880 this_sequence A006882 A006883 
               A006884
%K A006881 nonn,easy,nice
%O A006881 1,1
%A A006881 N. J. A. Sloane (njas(AT)research.att.com), Robert P. Munafo (mrob(AT)mrob.com), 
               Simon Plouffe (simon.plouffe(AT)gmail.com)

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