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A059890
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a(n) = |{m : multiplicative order of 8 mod m=n}|.
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11
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2, 4, 2, 18, 6, 24, 10, 72, 4, 84, 14, 462, 14, 128, 54, 672, 30, 124, 14, 4494, 82, 364, 14, 7608, 120, 172, 56, 9054, 62, 3920, 6, 5376, 238, 1500, 1518, 9600, 62, 364, 494, 69048, 30, 5892, 30, 24174, 956, 364, 62, 253280, 52, 12072, 222, 147246, 254, 12072
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OFFSET
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1,1
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COMMENTS
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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). a(n) = number of orders of degree-n monic irreducible polynomials over GF(8).
Also, number of primitive factors of 8^n - 1. - Max Alekseyev, May 03 2022
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LINKS
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FORMULA
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a(n) = Sum_{ d divides n } mu(n/d)*tau(8^d-1), (mu(n) = Moebius function A008683, tau(n) = number of divisors of n A000005).
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MAPLE
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with(numtheory):
a:= n-> add(mobius(n/d)*tau(8^d-1), d=divisors(n)):
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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