A007734 -id:A007734 - cp's OEIS frontend

A173933 The number of numbers m < k/2 such that m/k is a reduced fraction in the Cantor set, where k= A173931(n).

1, 2, 3, 3, 4, 8, 6, 15, 6, 6, 8, 15, 8, 12, 8, 8, 10, 24, 27, 16, 12, 9, 63, 10, 16, 12, 63, 20, 12, 11, 10, 36, 12, 56, 12, 12, 44, 12, 15, 36, 12, 16, 120, 60, 110, 24, 16, 18, 24, 225

Offset: 1

T. D. Noe, Mar 03 2010

nonn

When k is a prime of the form (3^r-1)/2, then the m are 2^r-1 numbers (greater than 0) whose base-3 representation consists of only 0's and 1's. Hence, for r=3,7, and 13, the primes k are 13, 1093, and 797161, and the number of m < k/2 is 3, 63, and 4095.

			When k=40, then 1/k, 3/k, 9/k, and 13/k have base-3 representations containing only the digits 0 and 2.

T. D. Noe, Table of n, a(n) for n = 1..185

Cf. A005823, A005836, A007734, A076481, A173931, A173934.

Length /@ Last[Transpose[cantor]] (* see A173931 *)

Name qualified by Peter Munn, Jul 14 2019

A336656 Numbers k not divisible by 3 such that the multiplicative order of 3 modulo k is squarefree.

Original entry on oeis.org

1, 2, 4, 7, 8, 11, 13, 14, 22, 23, 26, 28, 31, 43, 44, 46, 47, 49, 52, 56, 59, 61, 62, 67, 71, 77, 79, 83, 86, 88, 91, 92, 94, 98, 103, 104, 107, 118, 121, 122, 124, 131, 134, 139, 142, 143, 154, 157, 158, 161, 166, 167, 169, 172, 179, 182, 184, 188, 191, 196

Offset: 1

Amiram Eldar, Jul 28 2020

nonn

			2 is a term since the multiplicative order of 3 modulo 2 is 1 which is squarefree.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Francesco Pappalardi, Square free values of the order function, New York J. Math., Vol. 9 (2003), pp. 331-344.

Cf. A007734, A005117, A049149, A336654, A336655.

Select[Range[200], !Divisible[#, 3] && SquareFreeQ[MultiplicativeOrder[3, #]] &]

isok(k) = (k % 3) && issquarefree(znorder(Mod(3,k))); \\ Michel Marcus, Jul 29 2020

The number of terms not exceeding x is (a + o(1))* x * log(x)^(b-1), where a and b (~ 0.51175) are constants (Pappalardi, 2003).

cp's OEIS Frontend

A173933 The number of numbers m < k/2 such that m/k is a reduced fraction in the Cantor set, where k= A173931(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions