Search: id:A007862
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%I A007862
%S A007862 1,1,2,1,1,3,1,1,2,2,1,3,1,1,3,1,1,3,1,2,3,1,1,3,1,1,2,2,1,5,1,1,2,1,1,
%T A007862 4,1,1,2,2,1,4,1,1,4,1,1,3,1,2,2,1,1,3,2,2,2,1,1,5,1,1,3,1,1,4,1,1,2,2,
%U A007862 1,4,1,1,3,1,1,4,1,2,2,1,1,5,1,1,2,1,1,6,2,1,2,1,1,3,1,1,2,2,1,3,1,1,5
%N A007862 Number of triangular numbers that divide n.
%C A007862 Also a(n) is total number of ways to represent n+1 as a centered polygonal 
               number of the form km(m+1)/2+1 for k>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Apr 26 2007
%C A007862 a(A130317(n)) = n and a(m) <> n for m < A130317(n). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), May 23 2007
%C A007862 Number of oblong numbers that divide 2n. - Chandler
%H A007862 R. Zumkeller, <a href="b007862.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A007862 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CenteredPolygonalNumber.html">Centered Polygonal Number</a>.
%F A007862 Sum_{d|2*n,d+1|2*n} 1.
%F A007862 G.f.: sum(k=1, oo, 1/(1-x^A000217(k))) - Jon Perry (perry(AT)globalnet.co.uk), 
               Jul 03 2004
%F A007862 a(n) = A129308(2n). - Chandler
%t A007862 sup=90; TriN=Array[ (#+1)(#+2)/2&, Floor[ N[ Sqrt[ sup*2 ] ] ]-1 ]; Array[ 
               Function[n, 1+Count[ Map[ Mod[ n, # ]&, TriN ], 0 ] ], sup ]
%Y A007862 Cf. A046951.
%Y A007862 Sequence in context: A098824 A124032 A137457 this_sequence A055169 A010783 
               A083312
%Y A007862 Adjacent sequences: A007859 A007860 A007861 this_sequence A007863 A007864 
               A007865
%K A007862 nonn
%O A007862 1,3
%A A007862 R. P. Stanley [ rstan(AT)math.mit.edu ]
%E A007862 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008

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