A212957 -id:A212957 - cp's OEIS frontend

A218259 a(n) = |{m : multiplicative order of n mod m = 10}|.

0, 5, 16, 38, 47, 40, 66, 84, 150, 33, 72, 10, 106, 178, 168, 140, 265, 54, 534, 106, 68, 20, 296, 56, 564, 231, 732, 52, 730, 26, 604, 114, 80, 164, 348, 332, 297, 50, 912, 84, 904, 110, 88, 130, 222, 552, 332, 76, 1430, 81, 702, 236, 950, 178, 256, 168, 564

Offset: 1

Alois P. Heinz, Oct 24 2012

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Row n=10 of A212957.

Cf. A000005, A008683.

with(numtheory):
a:= n-> add(mobius(10/d) *tau(n^d-1), d={1, 2, 5, 10}):
seq(a(n), n=1..80);

a[n_] := Total[{1, -1, -1, 1} * DivisorSigma[0, n^{10, 5, 2, 1} - 1]]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jan 25 2025*)

a(n) = if(n == 1, 0, numdiv(n^10-1) - numdiv(n^5-1) - numdiv(n^2-1) + numdiv(n-1)); \\ Amiram Eldar, Jan 25 2025

a(n) = tau(n^10-1)-tau(n^5-1)-tau(n^2-1)+tau(n-1), with tau = A000005.

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

Original entry on oeis.org

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

Alois P. Heinz, Dec 21 2014

nonn

Main diagonal of A212957.

Cf. A000005, A008683.

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

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 *)

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

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.

cp's OEIS Frontend

A218259 a(n) = |{m : multiplicative order of n mod m = 10}|.

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