Search: id:A026416
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%I A026416
%S A026416 1,2,3,4,5,7,9,11,13,16,17,19,23,24,25,29,30,31,37,40,41,42,43,47,49,53,
               54,56,59,61,66,67,70,71,73,78,79,81,83,88,
%T A026416 89,97,101,102,103,104,105,107,109,110,113,114,121,127,128,130,131,135,
               136,137,138,139,149,151,152,154,157,163,165,167,169,
%U A026416 170,173,174,179,180,181,182,184,186,189,190,191,192,193,195,197,199,211,
               222,223,227,229,230,231,232,233,238,239,240,241
%N A026416 A 2-way classification of integers: a(1) = 1, a(2) = 2 and for n > 2, 
               a(n) is the smallest number not of the form a(i)*a(j) for 1 <= i 
               < j < n.
%C A026416 An equivalent definition is: a(1) = 1, a(2) = 2; and for n > 2, a(n) 
               = least positive integer > a(n-1) and not of the form a(i)*a(j) for 
               1 <= i < j < n.
%C A026416 A variant of A000028, differing only in the inclusion of 1.
%C A026416 This has a simpler definition than A000028, but the resulting pair lacks 
               the crucial property of the A000028/A000379 pair (see the comment 
               in A000028). - N. J. A. Sloane (njas(AT)research.att.com), Sep 28 
               2007
%C A026416 Contains (for example) 180, so is different from A123193. - Max Alekseyev, 
               Sep 20 2007
%e A026416 a(8) is not 10 because we already have 10 = 2*5. Of course all primes 
               appear. 16 appears because 16 is not a product of earlier terms.
%Y A026416 Complement of A131181. Cf. A000028.
%Y A026416 Cf. A066724, A026477, A050376, A084400.
%Y A026416 Sequence in context: A005706 A064175 A000028 this_sequence A123193 A066724 
               A079851
%Y A026416 Adjacent sequences: A026413 A026414 A026415 this_sequence A026417 A026418 
               A026419
%K A026416 nonn,easy
%O A026416 1,2
%A A026416 Clark Kimberling (ck6(AT)evansville.edu)
%E A026416 More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 23 2007
%E A026416 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 13 2008 at 
               the suggestion of R. J. Mathar and Max Alekseyev

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