A396407 Integers x such that there exist two integers 0<y<=z such that sigma(x)*psi(x)^2 = x^3 + y^3 + z^3.

5, 6, 24, 53, 58, 60, 102, 118, 197, 214, 216, 240, 258, 426, 445, 487, 491, 600, 668, 696, 861, 885, 1182, 1299, 1615, 1792, 2082, 2190, 2465, 2519, 2679, 3948, 3994, 4035, 4210, 4583, 4704, 5326, 5506, 5673, 5690, 6101, 6454, 7778, 7953, 8062, 8429, 8585, 8588, 9095, 10194, 11399, 12288, 12975, 13015

Offset

1,1

Comments

The numbers x, y and z form a sigma*psi^2-cubic triple.

Links

Table of n, a(n) for n=1..55.

S. I. Dimitrov, On σψ-quadratic k-tuples and related generalizations, hal-05303937, 2025.

Example

(60, 45, 147) is such a triple because sigma(60) * psi(60)^2 = 168 * 144^2 = 60^3 + 45^3 + 147^3.

Prog

(PARI)
dedekindpsi(n)=
{
  my(f = factor(n)[, 1]);
  n * prod(i = 1, #f, 1 + 1/f[i])
}
isok(x)=
{
  my(d = sigma(x) * dedekindpsi(x)^2 - x^3);
  for(y = 1, sqrtnint(d, 3),
    if((t = d - y^3) < y^3, break);
    if(ispower(t, 3), return(1))
  );
  0
}

Crossrefs

Cf. A000203, A001615, A003072, A385325, A391290, A396309.

Sequence in context: A042283 A047186 A324485 * A335827 A166591 A342610

Adjacent sequences: A396404 A396405 A396406 * A396408 A396409 A396411

Keyword

nonn

Author

S. I. Dimitrov, May 24 2026

Status

approved