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Search: id:A086933
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| A086933 |
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Number of non-congruent solutions to x^2 + y^2 = 0 mod n. |
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4
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| 1, 2, 1, 4, 9, 2, 1, 8, 9, 18, 1, 4, 25, 2, 9, 16, 33, 18, 1, 36, 1, 2, 1, 8, 65, 50, 9, 4, 57, 18, 1, 32, 1, 66, 9, 36, 73, 2, 25, 72, 81, 2, 1, 4, 81, 2, 1, 16, 49, 130, 33, 100, 105, 18, 9, 8, 1, 114, 1, 36, 121, 2, 9, 64, 225, 2, 1, 132, 1, 18, 1, 72, 145, 146, 65, 4, 1, 50, 1, 144, 81
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sum_{n<N} a(n) ~ (pi/(8*G))*N^2 as N approaches infinity, where G is Catalan's constant. - S. R. Finch (Steven.Finch(AT)inria.fr), Feb 05 2007
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REFERENCES
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N. Gafurov, On the number of divisors of a quadratic form, Proc. Steklov Inst. Math. 200 (1993) 137-148.
G. Yu, On the number of divisors of the quadratic form m^2+n^2, Canad. Math. Bull. 43 (2000) 239-256.
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LINKS
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S. Finch, Series involving arithmetric functions.
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FORMULA
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Multiplicative with a(2^e)=2^e, a(p^e)=p^(e-(e mod 2)) if p mod 4=3, a(p^e)=((p-1)*e+p)*p^(e-1) if p mod 4<>3 and p<>2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 22 2003
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CROSSREFS
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Cf. A062803.
Sequence in context: A133267 A076014 A120458 this_sequence A077878 A128058 A077160
Adjacent sequences: A086930 A086931 A086932 this_sequence A086934 A086935 A086936
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KEYWORD
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mult,nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 21 2003
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EXTENSIONS
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More terms from John W. Layman (layman(AT)math.vt.edu), Sep 22 2003
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