A397058 Integers x such that there exist four integers 0<y<=z<=t<=w such that sigma(x)*psi(x)^3*phi(x) = x^5 + y^5 + z^5 + t^5 + w^5.

12, 194, 342, 6000

Offset

1,1

Comments

The numbers x, y, z, t and w form a sigma*psi^3*phi-quintic quintuple.

Links

Table of n, a(n) for n=1..4.

S. I. Dimitrov, Python program (GitHub)

Example

(342, 54, 261, 315, 468) is such a quintuple because sigma(342) * psi(342)^3 * phi(342) = 780 * 720^3 * 108 = 342^5 + 54^5 + 261^5 + 315^5 + 468^5. Other quintuples are (12, 4, 4, 12, 16), (194, 19, 37, 83, 213) and (6000, 4320, 5180, 5700, 9400).

Prog

(Python) # See Links.

Crossrefs

Cf. A000010, A000203, A001615, A003350, A386672, A390006, A395737.

Sequence in context: A296841 A342111 A296942 * A159498 A034671 A066230

Adjacent sequences: A397055 A397056 A397057 * A397059 A397060 A397061

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Jun 15 2026

Status

approved