A218381 Numbers k such that A211996(k) is not zero.

3, 4, 8, 14, 15, 18, 20, 24, 28, 35, 39, 46, 48, 55, 60, 63, 64, 66, 68, 80, 84, 94, 99, 100, 114, 120, 124, 126, 128, 136, 138, 143, 144, 150, 154, 155, 156, 158, 168, 180, 183, 195, 196, 203, 220, 224, 234, 238, 240, 243, 255, 258, 260, 275, 284, 288, 291

Offset

1,1

Comments

For any n, the equation x^4 + a(n)*y^4 = z^2 is solvable in integers. - Arkadiusz Wesolowski, Aug 15 2013

The asymptotic density of this sequence is 0 (De Koninck et al., 2024). - Amiram Eldar, Nov 05 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

David Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. Vol. 34 (2), (1991), pp. 181-185.

Jean-Marie De Koninck, A. Arthur Bonkli Razafindrasoanaivolala, and Hans Schmidt Ramiliarimanana, Integers with a sum of co-divisors yielding a square, Research in Number Theory, Vol. 10, No. 2 (2024), Article 30; author's copy.

Mathematica

q[k_] := DivisorSum[k, 1 &, #^2 <= k && IntegerQ[Sqrt[# + k/#]] &] > 0; Select[Range[300], q] (* Amiram Eldar, Nov 05 2024 *)

Prog

(PARI) is(k) = k > 1 && fordiv(k, d, if(issquare(d + k/d), return(1)); if(d^2 > k, return(0))); \\ Amiram Eldar, Nov 05 2024

Crossrefs

Cf. A211996, A218382, A228880.

Sequence in context: A250473 A049893 A307043 * A103002 A310012 A181408

Adjacent sequences: A218378 A218379 A218380 * A218382 A218383 A218384

Keyword

nonn

Author

Michel Marcus, Oct 27 2012

Status

approved