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Search: id:A060968
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| A060968 |
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Number of non-congruent solutions of x^2 + y^2 == 1 mod n. |
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6
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| 1, 2, 4, 8, 4, 8, 8, 16, 12, 8, 12, 32, 12, 16, 16, 32, 16, 24, 20, 32, 32, 24, 24, 64, 20, 24, 36, 64, 28, 32, 32, 64, 48, 32, 32, 96, 36, 40, 48, 64, 40, 64, 44, 96, 48, 48, 48, 128, 56, 40, 64, 96, 52, 72, 48, 128, 80, 56, 60, 128, 60, 64, 96, 128, 48, 96, 68, 128, 96, 64, 72
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Multiplicative, with a(2^e) = 2 if e = 1 or 2^(e+1) if e > 1, a(p^e) = (p-1)p^(e-1) if p == 1 (mod 4), a(p^e) = (p+1)p^(e-1) if p == 3 (mod 4). - David W. Wilson (davidwwilson(AT)comcast.net), Jun 19 2001
a(n) = n * product{ 1 - 1/p, p is prime, p | n and p = 1 mod 4 } * product{ 1 + 1/p, p is prime, p | n and p = 3 mod 4 } * {2, if 4 | n } - Ola Veshta (olaveshta(AT)my-deja.com), May 18 2001
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EXAMPLE
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a(3) = 4 because the 4 solutions are: (0,1),(0,2),(1,0),(2,0)
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CROSSREFS
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Cf. A060594, A087784.
Sequence in context: A021805 A031401 A078479 this_sequence A016635 A133992 A126215
Adjacent sequences: A060965 A060966 A060967 this_sequence A060969 A060970 A060971
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jun 19 2001
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