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A129308
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a(n) = number of positive integers k such that k(k+1) divides n.
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7
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0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 5, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 2, 0, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| The usual OEIS policy is not to include sequences like this where alternate terms are zero; this is an exception.
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LINKS
| Ray Chandler, Table of n, a(n) for n=1..10000
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FORMULA
| a(2n-1) = 0; a(2n) = A007862(n). - Chandler
G.f.: sum(n>=1, x^(n*(n+1)/2)/(1-x^(n*(n+1)/2))). - Joerg Arndt, Jan 30 2011
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EXAMPLE
| The divisors of 20 are 1,2,4,5,10,20. Of these there are two that are of the form k(k+1): 2 = 1*2 and 20 = 4*5. So a(2) = 2.
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MATHEMATICA
| a = {}; For[n = 1, n < 90, n++, k = 1; co = 0; While[k < Sqrt[n], If[IntegerQ[ n/(k*(k + 1))], co++ ]; k++ ]; AppendTo[a, co]]; a - Stefan Steinerberger, May 27 2007
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CROSSREFS
| Cf. A007862.
Sequence in context: A035169 A067432 A192174 * A159200 A033764 A033784
Adjacent sequences: A129305 A129306 A129307 * A129309 A129310 A129311
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, May 26 2007
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 27 2007
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008
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