A273929 Numbers that are congruent to {5, 6, 7} mod 8 and are squarefree.

5, 6, 7, 13, 14, 15, 21, 22, 23, 29, 30, 31, 37, 38, 39, 46, 47, 53, 55, 61, 62, 69, 70, 71, 77, 78, 79, 85, 86, 87, 93, 94, 95, 101, 102, 103, 109, 110, 111, 118, 119, 127, 133, 134, 141, 142, 143, 149, 151, 157, 158, 159, 165, 166, 167, 173, 174

Offset: 1

Author

Frank M Jackson, Jun 04 2016

Keywords

• nonn

Comments

It has been shown, conditional on the Birch Swinnerton-Dyer conjecture, that this sequence is a subset of the primitive congruent numbers (A006991). The union of this sequence with A062695 gives A006991. Also this sequence is the intersection of A047574 and A005117.

The asymptotic density of this sequence is 3/Pi^2 (A104141). - Amiram Eldar, Mar 09 2021

Links

• Keith Conrad, The Congruent Number Problem, The Harvard College Mathematics Review, 2008.

Crossrefs

Cf. A005117, A006991, A047574, A062695, A104141.

Programs

Magma

[n: n in [1..250] | n mod 8 in [5, 6, 7] and IsSquarefree(n)]; // Vincenzo Librandi, Jun 06 2016

Mathematica

Select[Range[1000], MemberQ[{5, 6, 7}, Mod[#, 8]] && SquareFreeQ[#] &]

PARI

is(n) = n % 8 > 4 && issquarefree(n) \\ Felix Fröhlich, Jun 04 2016