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A007862
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Number of triangular numbers that divide n.
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8
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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, Apr 26 2007
a(A130317(n)) = n and a(m) <> n for m < A130317(n). - Reinhard Zumkeller, May 23 2007
Number of oblong numbers that divide 2n. - Chandler
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LINKS
| 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
| Sum_{d|2*n,d+1|2*n} 1.
G.f.: sum(k>=1, x^A000217(k)/(1-x^A000217(k))) - Jon Perry, Jul 03 2004
a(n) = A129308(2n). - Chandler
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MATHEMATICA
| 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
| Cf. A046951.
Sequence in context: A181651 A124032 A137457 * A055169 A205131 A175892
Adjacent sequences: A007859 A007860 A007861 * A007863 A007864 A007865
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KEYWORD
| nonn
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AUTHOR
| R. P. Stanley [ rstan(AT)math.mit.edu ]
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008
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