

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
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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^41)tau(n^21), 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_{dr} 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^41]DivisorSigma[0, n^21], {n, 70}] (* Harvey P. Dale, Nov 30 2011 *)


CROSSREFS

Cf. A059907, A059908, A059910A059916, A059499, A059885A059892, A002326, A053446A053453, 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



