A397440 Integers x such that there exist four integers 0<y<=z<=t<=w such that sigma(x)^2*psi(x)^2 = x^4 + y^4 + z^4 + t^4 + w^4.

20, 98, 148, 164, 180, 216, 260, 289, 332, 388, 432, 538, 556, 652, 964, 972

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..16.

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

S. I. Dimitrov, Python program (GitHub)

Example

(98, 32, 50, 78, 162) is such a quintuple because sigma(98)^2 * psi(98)^2 = 171^2 * 168^2 = 98^4 + 32^4 + 50^4 + 78^4 + 162^4.

Prog

(Python) # See Links.

Crossrefs

Cf. A000203, A001615, A386225, A391536, A397304.

Sequence in context: A039610 A177498 A157429 * A200470 A128676 A039455

Adjacent sequences: A397437 A397438 A397439 * A397441 A397442 A397444

Keyword

nonn,hard,more,new

Author

S. I. Dimitrov, Jun 25 2026

Status

approved