A385810 Integers x such that sigma(x)^2 - 3*x^2 is a square.

4, 6, 28, 45, 48, 60, 156, 208, 360, 496, 1170, 2016, 2520, 2925, 5733, 7605, 8128, 166617, 167580, 380160, 659044, 964080, 1085760, 1539900, 1571328, 1693440, 1778400, 2069613, 2224800, 2306304, 2410200, 2502720, 2522880, 4242420, 4311216, 4840192, 4917744, 4961484, 5331744, 5761536

Offset: 1

Author

Michel Marcus, Jul 09 2025

Keywords

• nonn

Links

• S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Crossrefs

Subsequence, with (x,x,x) triples, of A385531.

Cf. A000203.

Supersequence of A000396.

Programs

Mathematica

fQ[x_] := IntegerQ@ Sqrt[DivisorSigma[1, x]^2 - 3*x^2]; Select[Range[2^16], fQ] (* Michael De Vlieger, Jul 09 2025 *)

PARI

isok(x) = issquare(sigma(x)^2-3*x^2);