This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)