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A059889 a(n) = |{m : multiplicative order of 7 mod m=n}|. 3
4, 6, 8, 26, 4, 42, 12, 48, 52, 66, 12, 778, 4, 138, 80, 300, 12, 528, 12, 1430, 72, 138, 28, 15216, 24, 66, 1216, 966, 28, 3630, 28, 1344, 360, 58, 108, 16988, 28, 138, 176, 12752, 28, 7398, 12, 4422, 1900, 122, 12, 131028, 240, 536, 744, 1046, 28, 23744, 44 (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). a(n) = number of orders of degree n monic irreducible polynomials over GF(7).

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) = Sum_{d|n} mu(n/d)*tau(7^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(7^d-1), d=divisors(n)):

seq(a(n), n=1..40);  # Alois P. Heinz, Oct 12 2012

CROSSREFS

Cf. A000005, A008683, A058946, A053450, A058946, A059499, A059885-A059888, A059890-A059892, A212486.

Column k=7 of A212957. - Alois P. Heinz, Oct 12 2012

Sequence in context: A106366 A019160 A126233 * A058011 A278374 A300658

Adjacent sequences:  A059886 A059887 A059888 * A059890 A059891 A059892

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 06 2001

STATUS

approved

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Last modified March 24 11:34 EDT 2019. Contains 321448 sequences. (Running on oeis4.)