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Search: id:A007862
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| A007862 |
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Number of triangular numbers that divide n. |
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+0
6
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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
a(A130317(n)) = n and a(m) <> n for m < A130317(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 23 2007
Number of oblong numbers that divide 2n. - Chandler
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Centered Polygonal Number.
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FORMULA
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Sum_{d|2*n,d+1|2*n} 1.
G.f.: sum(k=1, oo, 1/(1-x^A000217(k))) - Jon Perry (perry(AT)globalnet.co.uk), Jul 03 2004
a(n) = A129308(2n). - Chandler
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MATHEMATICA
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sup=90; TriN=Array[ (#+1)(#+2)/2&, Floor[ N[ Sqrt[ sup*2 ] ] ]-1 ]; Array[ Function[n, 1+Count[ Map[ Mod[ n, # ]&, TriN ], 0 ] ], sup ]
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CROSSREFS
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Cf. A046951.
Sequence in context: A098824 A124032 A137457 this_sequence A055169 A010783 A083312
Adjacent sequences: A007859 A007860 A007861 this_sequence A007863 A007864 A007865
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KEYWORD
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nonn
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AUTHOR
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R. P. Stanley [ rstan(AT)math.mit.edu ]
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008
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