

A059908


a(n) = {m : multiplicative order of n mod m = 3}.


4



0, 1, 2, 4, 3, 2, 8, 2, 12, 5, 12, 2, 12, 2, 4, 20, 5, 6, 10, 2, 6, 14, 12, 2, 40, 9, 4, 6, 18, 10, 16, 6, 6, 8, 12, 12, 39, 2, 12, 8, 8, 6, 16, 6, 18, 26, 12, 6, 50, 3, 18, 8, 18, 2, 32, 12, 8, 20, 4, 6, 60, 2, 12, 26, 21, 4, 64, 10, 6, 8, 8, 6, 20, 14, 4, 12, 6, 4, 64, 2, 70, 7, 12, 6, 24
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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

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = tau(n^31)tau(n1), 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_{dr} mu(d)*tau(n^(r/d)1), where mu(n) = Moebius function A008683.


EXAMPLE

a(2) = {7} = 1, a(3) = {13,26} = 2, a(4) = {7,9,21,63} = 4, a(5) = {31,62,124} = 3, a(6) = {43,215} = 2, a(7) = {9,18,19,38,57,114,171,342} = 8,...


MATHEMATICA

Table[DivisorSigma[0, n^31]DivisorSigma[0, n1], {n, 90}] (* Harvey P. Dale, Feb 03 2015 *)


CROSSREFS

Cf. A059907, A059909A059916, A059499, A059885A059892, A002326, A053446A053453, A055205, A048691, A048785.
Row n=3 of A212957.  Alois P. Heinz, Oct 24 2012
Sequence in context: A212637 A283273 A269599 * A084936 A216842 A099066
Adjacent sequences: A059905 A059906 A059907 * A059909 A059910 A059911


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Feb 08 2001


STATUS

approved



