A386672 - OEIS

%I #26 Aug 04 2025 19:04:19

%S 46,94,946,1139,1680,3804,4200,29975,31143,48560,53428,63840,74178,

%T 121400,125280,135720,279300,483392,679952

%N 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.

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

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

%H S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024.

%H James Waldby, <a href="https://pat7.com/jp/s515-10007-t">A Table of Fifth Powers equal to a Fifth Power</a>

%e (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.

%e Other examples: (94, 38, 86, 92, 134), (946, 418, 1012, 1034, 1474), (1139, 323, 731, 782, 799), (63840, 144480, 154560, 157920, 225120).

%Y Cf. A000203, A003350, A063922, A386225.

%K nonn,hard,more

%O 1,1

%A _S. I. Dimitrov_, Jul 28 2025

%E More terms from _Michel Marcus_, Jul 29 2025