A081754 Numbers n such that the number of noncongruent solutions to x^(2^m) == 1 (mod n) is the same for any m>=1.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 18, 19, 21, 22, 23, 24, 27, 28, 31, 33, 36, 38, 42, 43, 44, 46, 47, 49, 54, 56, 57, 59, 62, 63, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84, 86, 88, 92, 93, 94, 98, 99, 103, 107, 108, 114, 118, 121, 124, 126, 127, 129, 131, 132, 133, 134

Offset: 1

Author

Benoit Cloitre, Apr 08 2003

Keywords

• nonn

Comments

Numbers n such that the multiplicative group of residues modulo n does not contain C4 as a subgroup. Equivalently, numbers not divisible by 16 or by any primes of the form 4k+1. - Ivan Neretin, Aug 02 2016

From Jianing Song, Oct 18 2021: (Start)

Numbers k such that psi(k) = A002322(k) is not divisible by 4.

Numbers k such that there are an odd number of coprime squares modulo k, i.e., numbers k such that A046073(k) is odd. (End)

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Modulo Multiplication Group.

Crossrefs

Cf. A060594, A002322, A046073.

Programs

Maple

filter:= n -> n mod 16 <> 0 and not member(1,numtheory:-factorset(n) mod 4):
select(filter, [$1..1000]); # Robert Israel, Aug 02 2016

Mathematica

Select[Range@135, ! Divisible[#, 16] && FreeQ[Mod[FactorInteger[3 #][[All, 1]], 4], 1] &] (* Ivan Neretin, Aug 02 2016 *)

PARI

isA081754(n) = if(n>2, znstar(n)[2][1]%4==2, 1) \\ Jianing Song, Oct 18 2021