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Squarefree numbers of the form m^2 + 4.
1

%I #21 Jun 27 2024 12:55:29

%S 5,13,29,53,85,173,229,293,365,445,533,629,733,965,1093,1229,1373,

%T 1685,1853,2029,2213,2405,2605,2813,3029,3253,3485,3973,4229,4493,

%U 4765,5045,5333,5629,5933,6245,6565,6893,7229,7573,8285,8653,9029,9413,9805

%N Squarefree numbers of the form m^2 + 4.

%C Yokoi's conjecture posits that, except for most of the values less than 365, the ring of algebraic integers of Q(sqrt(a(n)) has class number greater than 1. Only one counterexample to this conjecture may exist, and it would also be a counterexample to the generalized Riemann hypothesis, according to Mollin (1996).

%C All terms == 5 (mod 8). - _Robert Israel_, Jun 05 2019

%D Richard A. Mollin, Quadratics. Boca Raton, Florida: CRC Press (1996): 176 - 177.

%H Robert Israel, <a href="/A308464/b308464.txt">Table of n, a(n) for n = 1..10000</a>

%p select(numtheory:-issqrfree,[seq(m^2+4,m=1..1000,2)]); # _Robert Israel_, Jun 05 2019

%t Select[(2Range[50] - 1)^2 + 4, MoebiusMu[#] != 0 &]

%t Select[Table[i^2 + 4, {i, 1, 100}], SquareFreeQ] (* _Navvye Anand_, Jun 20 2024 *)

%o (PARI) is(n) = issquarefree(n) && issquare(n-4) \\ _Felix Fröhlich_, May 29 2019

%Y Cf. A078370, A087475 (supersequences).

%K nonn,easy

%O 1,1

%A _Alonso del Arte_, May 29 2019