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A111861
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a(n) is the number of integers of the form (n+k)/(n-k)^2 for k>0.
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0
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1, 2, 2, 5, 2, 4, 4, 4, 2, 4, 4, 4, 3, 4, 3, 7, 2, 4, 3, 4, 2, 7, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 2, 6, 3, 5, 4, 4, 3, 6, 3, 4, 4, 4, 2, 6, 3, 4, 3, 4, 3, 6, 2, 4, 3, 6, 2, 6, 3, 4, 5, 4, 3, 4, 2, 5, 6, 4, 3, 6, 4, 4, 2, 4, 3, 6, 2, 5, 6, 4, 2, 4, 3, 4, 3, 5, 3, 6, 2, 4, 4, 6, 3, 6, 3, 5, 3, 4, 3, 4, 3, 4, 4, 4, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| First occurrence of n [0,500] is at a(k): 0,1,12,5,3,33,15,210,105, ..., . - Robert G. Wilson v (rgwv(at)rgwv.com), Nov 23 2005
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EXAMPLE
| For n=14 we have integer value for the form when k={13; 15; 18} and (14+k)/(14-k)^2 = {27, 29, 2}. Thus a(14) = 3
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MATHEMATICA
| f[n_] := Length[Select[(n + #)/(n - #)^2 & /@ Range[n^2 + 3], IntegerQ[ # ] &]]; Array[f, 105] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A111150, A111164.
Sequence in context: A133501 A124316 A061034 * A004543 A153078 A076200
Adjacent sequences: A111858 A111859 A111860 * A111862 A111863 A111864
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KEYWORD
| easy,nonn
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Nov 22 2005
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EXTENSIONS
| Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Nov 23 2005
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