

A273929


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


5



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
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OFFSET

1,1


COMMENTS

It has been shown, conditional on the Birch SwinnertonDyer 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.


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 FrÃ¶hlich, 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.
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



