This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
18^6 = 2^6 + 5^6 + 5^6 + 5^6 + 7^6 + 7^6 + 9^6 + 9^6 + 10^6 + 14^6 + 17^6. 19^6 = 1^6 + 7^6 + 7^6 + 7^6 + 8^6 + 12^6 + 13^6 + 13^6 + 13^6 + 13^6 + 17^6. 30^6 = 1^6 + 2^6 + 7^6 + 7^6 + 9^6 + 12^6 + 17^6 + 17^6 + 19^6 + 23^6 + 28^6. 31^6 = 3^6 + 4^6 + 7^6 + 7^6 + 11^6 + 11^6 + 13^6 + 13^6 + 23^6 + 25^6 + 28^6. 32^6 = 7^6 + 7^6 + 7^6 + 17^6 + 17^6 + 17^6 + 18^6 + 20^6 + 20^6 + 25^6 + 29^6. 33^6 = 1^6 + 4^6 + 4^6 + 6^6 + 10^6 + 14^6 + 20^6 + 20^6 + 24^6 + 28^6 + 28^6. 34^6 = 1^6 + 1^6 + 2^6 + 5^6 + 7^6 + 7^6 + 12^6 + 17^6 + 23^6 + 28^6 + 31^6. 36^6 = 1^6 + 1^6 + 1^6 + 7^6 + 14^6 + 14^6 + 19^6 + 19^6 + 19^6 + 30^6 + 33^6.
(24, 24, 36, 48, 48) is such a quintuple because sigma(24)^4 = sigma(24)^4 = 60^4 = 24^4 + 24^4 + 36^4 + 48^4 + 48^4. (240, 240, 240, 408, 720) and (600, 600, 600, 1020, 1800) are the two next quintuples.
find4(ss) = my(v=List(), k, t); ss\=1; for(x=1, sqrtnint(ss-2, 4), for(y=1, min(sqrtnint(ss-x^4-1, 4), x), k=x^4+y^4; for(z=1, min(sqrtnint(ss-k, 4), y), if (k+z^4==ss, return([x,y,z]))))); isok4(x) = my(s=sigma(x), v=select(z->(z>=x), invsigma(s))); if (#v >=2, for (i=1, #v, my(k=s^4 - x^4 - v[i]^4); if (k>0, my(xyz = find4(k)); if (xyz, return([x, v[i], xyz[1], xyz[2], xyz[3]]));););); \\ Michel Marcus, Jul 22 2025
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