A391536 Integers x such that there exist four integers 0<y<=z<=t<=w such that psi(x)^4 = x^4 + y^4 + z^4 + t^4 + w^4.

538, 34432, 68864, 137728, 275456, 550912

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..6.

S. I. Dimitrov, On psi-quadratic k-tuples and their generalizations, arXiv:2509.18291 [math.NT], 2025.

Example

(538, 96, 532, 548, 648) is such a quintuple because psi(538)^4 = 810^4 = 538^4 + 96^4 + 532^4 + 548^4 + 648^4.

Crossrefs

Cf. A001615, A297305, A386225.

Sequence in context: A252339 A224742 A231194 * A367525 A111258 A239347

Adjacent sequences: A391533 A391534 A391535 * A391537 A391538 A391539

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Dec 12 2025

Status

approved