

A059907


a(n) = {m : multiplicative order of n mod m = 2}.


6



0, 1, 2, 2, 5, 2, 6, 4, 6, 3, 12, 2, 10, 6, 8, 4, 13, 2, 18, 6, 10, 4, 16, 4, 12, 9, 12, 4, 26, 2, 20, 6, 8, 12, 20, 4, 15, 6, 16, 4, 32, 2, 24, 10, 10, 6, 20, 4, 26, 9, 18, 4, 26, 6, 32, 12, 12, 4, 28, 2, 20, 10, 12, 18, 25, 4, 24, 6, 26, 4, 52, 2, 18, 10, 12, 18, 26, 4, 40, 8, 14, 5, 28
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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^21)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) = {3} = 1, a(3) = {4,8} = 2, a(4) = {5,15} = 2, a(5) = {3,6,8,12,24} = 5, a(6) = {7,35} = 2, a(7) = {4,8,12,16,24,48} = 6,...


MAPLE

with(numtheory):f := n>tau(n^21)tau(n1):for n from 1 to 100 do printf(`%d, `, f(n)) od:


CROSSREFS

Cf. A059908A059916, A059499, A059885A059892, A002326, A053446A053453, A055205, A048691, A048785.
Row n=2 of A212957.  Alois P. Heinz, Oct 24 2012
Sequence in context: A294339 A185291 A018216 * A024931 A256612 A029648
Adjacent sequences: A059904 A059905 A059906 * A059908 A059909 A059910


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Feb 08 2001


STATUS

approved



