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

1,1

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

Table of n, a(n) for n=1..57.

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

Mathematica

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

Prog

(PARI) is(n) = n % 8 > 4 && issquarefree(n) \\ Felix Fröhlich, Jun 04 2016
(Magma) [n: n in [1..250] | n mod 8 in [5, 6, 7] and IsSquarefree(n)]; // Vincenzo Librandi, Jun 06 2016

Crossrefs

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

Sequence in context: A003273 A006991 A047574 * A067531 A031029 A134985

Adjacent sequences: A273926 A273927 A273928 * A273930 A273931 A273932

Keyword

nonn

Author

Frank M Jackson, Jun 04 2016

Status

approved