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A059888 a(n) = |{m : multiplicative order of 6 mod m=n}|. 4
2, 2, 2, 4, 4, 10, 2, 8, 12, 40, 6, 108, 6, 42, 40, 48, 30, 100, 6, 332, 10, 22, 30, 376, 26, 118, 48, 332, 2, 1436, 6, 448, 54, 222, 88, 7952, 62, 54, 54, 2680, 6, 698, 30, 476, 1476, 222, 14, 7632, 28, 438, 478, 1916, 14, 1872, 84, 11896, 118, 58, 14, 784452 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..60.

FORMULA

a(n) = Sum_{ d divides n } mu(n/d)*tau(6^d-1), (mu(n) = Moebius function A008683, tau(n) = number of divisors of n A000005).

MAPLE

with(numtheory):

a:= n-> add(mobius(n/d)*tau(6^d-1), d=divisors(n)):

seq(a(n), n=1..50);  # Alois P. Heinz, Oct 12 2012

CROSSREFS

Cf. A000005, A008683, A053449, A059499, A059885, A059886, A059888-A059892.

Column k=6 of A212957. - Alois P. Heinz, Oct 12 2012

Sequence in context: A010238 A178799 A089819 * A299204 A230141 A151680

Adjacent sequences:  A059885 A059886 A059887 * A059889 A059890 A059891

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 06 2001

STATUS

approved

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Last modified November 15 10:31 EST 2018. Contains 317237 sequences. (Running on oeis4.)