A252760 Number of moduli m such that the multiplicative order of n mod m equals n.

0, 1, 2, 4, 9, 10, 12, 72, 112, 33, 12, 212, 42, 22, 108, 96, 35, 456, 6, 1912, 714, 220, 60, 5364, 4032, 747, 448, 3944, 762, 24370, 8, 5376, 738, 8148, 996, 253568, 1143, 242, 980, 46032, 248, 65138, 56, 23004, 195768, 282, 28, 386736, 327520, 12102, 24366

Offset

1,3

Links

Table of n, a(n) for n=1..51.

Formula

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

a(n) = Sum_{d|n} mu(n/d)*tau(n^d-1), mu = A008683, tau = A000005.

Maple

with(numtheory):
a:= n-> add(mobius(n/d)*tau(n^d-1), d=divisors(n)):
seq(a(n), n=1..30);

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#]*DivisorSigma[0, n^#-1]&]; a[1] = 0;
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 46}] (* Jean-François Alcover, Mar 25 2017, translated from Maple *)

Prog

(PARI) a(n) = if (n==1, 1, sumdiv(n, d, moebius(n/d)*numdiv(n^d-1))); \\ Michel Marcus, Mar 25 2017

Crossrefs

Main diagonal of A212957.

Cf. A000005, A008683.

Sequence in context: A047465 A365343 A002258 * A191766 A287518 A287526

Adjacent sequences: A252757 A252758 A252759 * A252761 A252762 A252763

Keyword

nonn

Author

Alois P. Heinz, Dec 21 2014

Status

approved