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A066743
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a(n) is the number of integers of the form (n^2+1)/(k^2+1) k=1,2,3,...,n.
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3
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1, 1, 3, 1, 2, 1, 4, 2, 2, 1, 2, 2, 5, 1, 2, 1, 5, 3, 2, 1, 4, 2, 4, 1, 2, 1, 4, 2, 2, 2, 4, 2, 4, 1, 2, 1, 4, 3, 2, 1, 2, 2, 6, 1, 2, 1, 9, 2, 2, 1, 2, 2, 4, 1, 3, 1, 8, 2, 2, 1, 2, 2, 4, 2, 2, 1, 4, 3, 2, 1, 2, 3, 7, 1, 2, 1, 4, 2, 2, 2, 3, 2, 7, 1, 2, 1, 4, 2, 3, 1, 4, 2, 5, 1, 2, 1, 4, 3, 4, 1, 2, 2, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| Conjecture: (1/n)*sum(i=1, n, a(i))=c*ln(ln(n)) asymptotically with 1<c<2.
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MATHEMATICA
| a[ n_ ] := Length[ Select[ Range[ 1, n ], IntegerQ[ (n^2+1)/(#^2+1) ]& ] ]
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CROSSREFS
| Sequence in context: A166866 A177343 A124036 * A203531 A046645 A016470
Adjacent sequences: A066740 A066741 A066742 * A066744 A066745 A066746
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 16 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 20 2002
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