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

Author

Michel Marcus, Oct 27 2012

Keywords

• nonn

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.

Crossrefs

Cf. A211996, A218382, A228880.

Programs

Mathematica

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

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