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A059889
a(n) = |{m : multiplicative order of 7 mod m=n}|.
16
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
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).
Also, number of primitive factors of 7^n - 1 (cf. A218358). - Max Alekseyev, May 03 2022
LINKS
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
Number of primitive factors of b^n - 1: A059499 (b=2), A059885(b=3), A059886 (b=4), A059887 (b=5), A059888 (b=6), this sequence (b=7), A059890 (b=8), A059891 (b=9), A059892 (b=10).
Column k=7 of A212957.
Sequence in context: A106366 A019160 A126233 * A058011 A278374 A300658
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 06 2001
STATUS
approved