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Search: id:A059907
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| A059907 |
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a(n) = |{m : multiplicative order of n mod m = 2}|. |
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+0
5
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| 0, 1, 2, 2, 5, 2, 6, 4, 6, 3, 12, 2, 10, 6, 8, 4, 13, 2, 18, 6, 10, 4, 16, 4, 12, 9, 12, 4, 26, 2, 20, 6, 8, 12, 20, 4, 15, 6, 16, 4, 32, 2, 24, 10, 10, 6, 20, 4, 26, 9, 18, 4, 26, 6, 32, 12, 12, 4, 28, 2, 20, 10, 12, 18, 25, 4, 24, 6, 26, 4, 52, 2, 18, 10, 12, 18, 26, 4, 40, 8, 14, 5, 28
(list; graph; listen)
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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^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) = |{3}| = 1, a(3) = |{4,8}| = 2, a(4) = |{5,15}| = 2, a(5) = |{3,6,8,12,24}| = 5, a(6) = |{7,35}| = 2, a(7) = |{4,8,12,16,24,48}| = 6,...
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MAPLE
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with(numtheory):f := n->tau(n^2-1)-tau(n-1):for n from 1 to 100 do printf(`%d, `, f(n)) od:
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CROSSREFS
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Cf. A059908-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.
Sequence in context: A093663 A011143 A018216 this_sequence A024931 A029648 A126103
Adjacent sequences: A059904 A059905 A059906 this_sequence A059908 A059909 A059910
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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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