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Search: id:A059909
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| A059909 |
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a(n) = |{m : multiplicative order of n mod m = 4}|. |
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+0
3
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| 0, 2, 6, 4, 12, 4, 26, 18, 14, 6, 24, 12, 64, 8, 16, 8, 66, 20, 36, 8, 64, 24, 76, 6, 28, 12, 64, 24, 48, 12, 100, 40, 50, 48, 36, 8, 96, 40, 28, 8, 104, 12, 208, 36, 24, 36, 200, 18, 48, 36, 36, 24, 128, 8, 152, 16, 172, 24, 48, 12, 48, 36, 56, 72, 40, 8, 128, 56, 48, 40
(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^4-1)-tau(n^2-1), where tau(n) = number of divisors of n A000005. More 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) = |{5, 15}| = 2, a(3) = |{5, 10, 16, 20, 40, 80}| = 6, a(4) = |{17, 51, 85, 255}| = 4, a(5) = |{13, 16, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624}| = 12, ...
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CROSSREFS
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Cf. A059907, A059908, A059910-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.
Sequence in context: A065879 A065880 A090546 this_sequence A145177 A007517 A072946
Adjacent sequences: A059906 A059907 A059908 this_sequence A059910 A059911 A059912
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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.rs), Feb 08 2001
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