A386672 Integers x such that there exist four integers 0<y<=z<=t<=w such that sigma(x)^5 = x^5 + y^5 + z^5 + t^5 + w^5.

46, 94, 946, 1139, 1680, 3804, 4200, 29975, 31143, 48560, 53428, 63840, 74178, 121400, 125280, 135720, 279300, 483392, 679952

Offset

1,1

Comments

The numbers x, y, z, t and w form a sigma-quintic quintuple.

Other terms of the sequence: 5446350, 20201728, 326481408.

Links

Table of n, a(n) for n=1..19.

S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

James Waldby, A Table of Fifth Powers equal to a Fifth Power

Example

(46, 19, 43, 47, 67) is such a quintuple because sigma(46)^5 = 72^5 = 46^5 + 19^5 + 43^5 + 47^5 + 67^5.
Other examples: (94, 38, 86, 92, 134), (946, 418, 1012, 1034, 1474), (1139, 323, 731, 782, 799), (63840, 144480, 154560, 157920, 225120).

Crossrefs

Cf. A000203, A003350, A063922, A386225.

Sequence in context: A007630 A004923 A260568 * A044184 A044565 A252695

Adjacent sequences: A386669 A386670 A386671 * A386673 A386674 A386675

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Jul 28 2025

Extensions

More terms from Michel Marcus, Jul 29 2025

Status

approved