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Search: id:A059911
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| A059911 |
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a(n) = |{m : multiplicative order of n mod m = 6}|. |
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+0
2
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| 0, 3, 10, 16, 37, 10, 42, 24, 58, 53, 164, 26, 68, 38, 32, 68, 169, 22, 222, 38, 42, 50, 328, 40, 180, 219, 108, 26, 334, 82, 460, 82, 92, 72, 220, 108, 449, 86, 128, 80, 192, 22, 336, 110, 222, 218, 540, 84, 778, 129, 150, 80, 270, 54, 328, 356, 132, 68, 348, 22
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The multiplicative order of a mod m, gcd(a,m) = 1, is the smallest natural number d for which a^d = 1 (mod m).
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FORMULA
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a(n) = tau(n^6-1)-tau(n^3-1)-tau(n^2-1)+tau(n-1), where tau(n) = number of divisors of n A000005. Generally, if b(n, r) = |{m : multiplicative order of n mod m = r}| then b(n, r) = Sum_{d|r} mu(d)*tau(n^(r/d)-1), where mu(n) = Moebius function A008683.
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EXAMPLE
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a(2) = |{9,21,63}| = 3, a(3) = |{7,14,28,52,56,91,104,182,364,728}| = 10, a(4) = |{13,35,39,45,65,91,105,117,195,273,315,455,585,819,1365,4095}| = 16,...
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CROSSREFS
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Cf. A059907-A059910, A059911-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.
Sequence in context: A063209 A063109 A083684 this_sequence A043405 A063293 A024981
Adjacent sequences: A059908 A059909 A059910 this_sequence A059912 A059913 A059914
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 08 2001
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