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Search: id:A059910
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| A059910 |
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a(n) = |{m : multiplicative order of n mod m = 5}|. |
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+0
3
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| 0, 1, 4, 6, 9, 4, 4, 6, 20, 9, 8, 2, 6, 6, 12, 44, 5, 6, 18, 14, 12, 4, 4, 2, 56, 13, 20, 4, 6, 2, 40, 6, 18, 12, 12, 44, 63, 6, 28, 4, 16, 14, 8, 2, 18, 12, 28, 14, 70, 3, 42, 12, 42, 6, 24, 8, 56, 44, 60, 6, 60, 2, 4, 90, 21, 20, 24, 2, 18, 60, 88, 6, 12, 2, 28, 26, 6, 28, 8, 14, 170
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OFFSET
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1,3
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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^5-1)-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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CROSSREFS
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Cf. A059907-A059909, A059911-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.
Sequence in context: A106146 A129112 A076418 this_sequence A019837 A132160 A021217
Adjacent sequences: A059907 A059908 A059909 this_sequence A059911 A059912 A059913
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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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