Search: id:A010766
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%I A010766
%S A010766 1,2,1,3,1,1,4,2,1,1,5,2,1,1,1,6,3,2,1,1,1,7,3,2,1,1,1,1,8,4,2,2,1,
%T A010766 1,1,1,9,4,3,2,1,1,1,1,1,10,5,3,2,2,1,1,1,1,1,11,5,3,2,2,1,1,1,1,1,1,
%U A010766 12,6,4,3,2,2,1,1,1,1,1,1,13,6,4,3,2,2,1,1,1,1,1,1,1
%N A010766 Triangle of numbers [ n/k ], k=1..n.
%C A010766 Number of times k occurs as divisor of numbers not greater than n. - 
               Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 19 2004
%C A010766 Viewed as a partition, row n is the smallest partition that contains 
               every partition of n. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Mar 11 2006
%C A010766 Row sums = A006218 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 30 2007
%C A010766 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 30 2009: 
               (Start)
%C A010766 A014668 = eigensequence of the triangle. A163313 = A010766 * A014668
%C A010766 (diagonalized) as an infinite lower triangular matrix) (End)
%H A010766 T. D. Noe, <a href="b010766.txt">Rows n=1..50 of triangle, flattened</
               a>
%F A010766 G.f.: 1/(1-x)*Sum_(k>=1} x^k/(1-y*x^k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Feb 05 2004
%F A010766 Triangle A010766 = A000012 * A051731 as infinite lower triangular matrices. 
               - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 30 2007
%F A010766 Equals A000012 * A051731 as infinite lower triangular matrices. - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Nov 14 2007
%e A010766 1; 2,1; 3,1,1; 4,2,1,1; 5,2,1,1,1; ...
%Y A010766 Another version of A003988.
%Y A010766 Cf. A013942. Also ... A033330, ...
%Y A010766 Cf. A006218, A115725.
%Y A010766 T(n, 1)=n, T(n, 2)=A008619(n-2) for n>1, T(n, 3)=A008620(n-3) for n>2, 
               T(n, 4)=A008621(n-4) for n>3, T(n, 5)=A002266(n) for n>4, T(n, n)=1.
%Y A010766 Cf. A051731, A006218.
%Y A010766 Cf. A051731, A000012.
%Y A010766 A014668, A163313 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 30 
               2009]
%Y A010766 Sequence in context: A143349 A088425 A141294 this_sequence A135841 A089178 
               A116599
%Y A010766 Adjacent sequences: A010763 A010764 A010765 this_sequence A010767 A010768 
               A010769
%K A010766 nonn,tabl,easy,nice
%O A010766 1,2
%A A010766 N. J. A. Sloane (njas(AT)research.att.com).

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