A385397 - OEIS

%I #15 Jul 01 2025 23:17:18

%S 153,216,255,324,672,735,1074,1170,1218,2430,2655,2736,3482,4148,4605,

%T 4935,5220,5446,5916,6048,7140,9340,11000,11160,12768,14090,14098,

%U 14980,17220,17696,18984,21068,21948,22128,23022,23205,24297,24570,25284,25740,29058,29640,30240,30690,31008,31190,32760,37140,39840

%N Numbers x such that there exist three integers 0<x<=y, z>0 and w>0 such that sigma(x)^3 = sigma(y)^3 = x^3 + y^3 + z^3 + w^3.

%C The numbers x, y, z and w form a sigma-cubic quadruple. See Dimitrov link.

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

%e (255, 321, 84, 312) is such a quadruple because sigma(255)^3 = sigma(321)^3 = 432^3 = 255^3 + 321^3 + 84^3 + 312^3.

%o (PARI) issc(n) = if (n>0, for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1))); \\ A003325

%o isok(x) = my(s=sigma(x)); for (y=1, x, if (s == sigma(y), if (issc(s^3-x^3-y^3), return(1)););); \\ _Michel Marcus_, Jun 27 2025

%Y Cf. A000203, A385325, A385356.

%K nonn,hard

%O 1,1

%A _S. I. Dimitrov_, Jun 27 2025

%E More terms from _David A. Corneth_, Jun 27 2025