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A059909 a(n) = |{m : multiplicative order of n mod m = 4}|. 3
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; refs; listen; history; text; internal format)
OFFSET

1,2

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..70.

FORMULA

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.

EXAMPLE

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, ...

MATHEMATICA

Table[DivisorSigma[0, n^4-1]-DivisorSigma[0, n^2-1], {n, 70}] (* Harvey P. Dale, Nov 30 2011 *)

CROSSREFS

Cf. A059907, A059908, A059910-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.

Sequence in context: A242901 A266013 A222423 * A145177 A007517 A072946

Adjacent sequences:  A059906 A059907 A059908 * A059910 A059911 A059912

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 08 2001

STATUS

approved

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Last modified May 28 12:19 EDT 2017. Contains 287241 sequences.