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A059910 a(n) = |{m : multiplicative order of n mod m = 5}|. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The multiplicative order of a mod m, gcd(a,m) = 1, is the smallest natural number d for which a^d = 1 (mod m).

LINKS

Table of n, a(n) for n=1..81.

FORMULA

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.

CROSSREFS

Cf. A059907-A059909, A059911-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.

Sequence in context: A210616 A238167 A076418 * A019837 A132160 A021217

Adjacent sequences:  A059907 A059908 A059909 * A059911 A059912 A059913

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 08 2001

STATUS

approved

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Last modified March 19 13:03 EDT 2019. Contains 321330 sequences. (Running on oeis4.)