A308464 Squarefree numbers of the form m^2 + 4.

5, 13, 29, 53, 85, 173, 229, 293, 365, 445, 533, 629, 733, 965, 1093, 1229, 1373, 1685, 1853, 2029, 2213, 2405, 2605, 2813, 3029, 3253, 3485, 3973, 4229, 4493, 4765, 5045, 5333, 5629, 5933, 6245, 6565, 6893, 7229, 7573, 8285, 8653, 9029, 9413, 9805

Offset: 1

Author

Alonso del Arte, May 29 2019

Keywords

• nonn
• easy

Comments

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).

All terms == 5 (mod 8). - Robert Israel, Jun 05 2019

References

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A078370, A087475 (supersequences).

Programs

Maple

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

Mathematica

Select[(2Range[50] - 1)^2 + 4, MoebiusMu[#] != 0 &]
Select[Table[i^2 + 4, {i, 1, 100}], SquareFreeQ] (* Navvye Anand, Jun 20 2024 *)

PARI

is(n) = issquarefree(n) && issquare(n-4) \\ Felix Fröhlich, May 29 2019