A397301 Integers x such that there exist four integers 0<x<=y<=z and 0<t<=w such that sigma(x)*psi(x)^2 = sigma(y)*psi(y)^2 = sigma(z)*psi(z)^2 = x^3 + y^3 + z^3 + t^3 + w^3.

24, 30, 62, 174, 216, 238, 357, 420, 756, 1146, 3240, 3382

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..12.

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

S. I. Dimitrov, Python program (GitHub)

Example

(174, 190, 323, 5, 94) is such a quintuple because sigma(174) * psi(174)^2 = sigma(190) * psi(190)^2 = sigma(323) * psi(323)^2 = 360 * 360^2 = 174^3 + 190^3 + 323^3 + 5^3 + 94^3.

Prog

(Python) # See Links.

Crossrefs

Cf. A000203, A001615, A003328, A386378, A391535, A396564, A396407, A397251.

Sequence in context: A372991 A333122 A391131 * A138601 A135045 A109321

Adjacent sequences: A397294 A397295 A397297 * A397302 A397303 A397304

Keyword

nonn,more

Author

S. I. Dimitrov, Jun 20 2026

Status

approved