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.
%I A386727 #16 Aug 06 2025 18:57:08 %S A386727 3,10,24,51,78,105,114,136,186,220,224,255,322,348,357,370,435,478, %T A386727 506,616,642,710,748,820,861,885,957,996,1004,1068,1113,1214,1221, %U A386727 1276,1292,1336,1390,1485,1491,1562,1564,1581,1605,1660,1670,1704,1716,1724,1815,1869,1880,1912,1947 %N A386727 Numbers x such that there exist three integers 0<x<=y<=z<=t such that sigma(x) = sigma(y) = sigma(z) = sigma(t) = (x + y + z + t)/3. %C A386727 The numbers x, y, z and t form an amicable quadruple according to Yanney’s definition. %H A386727 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp). %H A386727 Benjamin Franklin Yanney, <a href="https://www.jstor.org/stable/2300268">Another definition of amicable numbers and some of their relations to Dickson's amicables</a>, Amer. Math. Monthly, Vol. 30, No. 6 (1923), 311-315. %e A386727 114 is in the sequence since sigma(114) = sigma(158) = sigma(209) = sigma(239) = 240 = (114 + 158 + 209 + 239)/3. %o A386727 (PARI) isok(x1) = my(s=sigma(x1), vx=select(x->(x>=x1), invsigma(s)), v=vector(4, i, vx[1])); for (i=1, #vx, v[2] = vx[i]; for (j=1, #vx, v[3] = vx[j]; for (k=1, #vx, v[4] = vx[k]; if (vecsum(v) == 3*s, return(1));););); \\ _Michel Marcus_, Aug 01 2025 %Y A386727 Cf. A000203, A036471, A386726. %K A386727 nonn %O A386727 1,1 %A A386727 _S. I. Dimitrov_, Jul 31 2025 %E A386727 More terms from _Michel Marcus_, Aug 01 2025