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A059892 a(n) = |{m : multiplicative order of 10 mod m is equal to n}|. 20
3, 3, 5, 6, 9, 53, 9, 36, 12, 33, 9, 186, 21, 33, 111, 144, 9, 564, 3, 330, 239, 273, 3, 1756, 84, 165, 76, 714, 93, 16167, 21, 5952, 111, 177, 363, 4288, 21, 15, 99, 5724, 45, 48807, 45, 4314, 1140, 183, 9, 14192, 36, 2940, 495, 1338, 45, 11572, 747, 11484 (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).

The number of unit fractions 1/k having a decimal expansion of period n and with k coprime to 10. - T. D. Noe, May 18 2007

LINKS

Ray Chandler, Table of n, a(n) for n = 1..322 (first 280 terms from T. D. Noe)

FORMULA

a(n) = Sum_{d|n} mu(n/d)*tau(10^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(10^d-1), d=divisors(n)):

seq(a(n), n=1..30);  # Alois P. Heinz, Oct 12 2012

MATHEMATICA

f[n_, d_] := MoebiusMu[n/d]*Length[Divisors[10^d - 1]]; a[n_] := Total[(f[n, #] & ) /@ Divisors[n]]; Table[a[n], {n, 1, 56}] (* Jean-François Alcover, Mar 21 2011 *)

PROG

(PARI) j=[]; for(n=1, 70, j=concat(j, sumdiv(n, d, moebius(n/d)*numdiv(10^d-1)))); j

(Python)

from sympy import divisors, mobius, divisor_count

def a(n): return sum([mobius(n/d)*divisor_count(10**d - 1) for d in divisors(n)]) # Indranil Ghosh, Apr 23 2017

CROSSREFS

Cf. A000005, A008683, A053453, A058946, A059499, A059885-A059891, A070528.

Column k=10 of A212957.

Sequence in context: A060022 A187679 A048274 * A241090 A091607 A276434

Adjacent sequences:  A059889 A059890 A059891 * A059893 A059894 A059895

KEYWORD

easy,nonn,nice

AUTHOR

Vladeta Jovovic, Feb 06 2001

EXTENSIONS

More terms from Jason Earls, Aug 06 2001

STATUS

approved

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Last modified February 19 12:31 EST 2019. Contains 320310 sequences. (Running on oeis4.)