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.

3, 10, 24, 51, 78, 105, 114, 136, 186, 220, 224, 255, 322, 348, 357, 370, 435, 478, 506, 616, 642, 710, 748, 820, 861, 885, 957, 996, 1004, 1068, 1113, 1214, 1221, 1276, 1292, 1336, 1390, 1485, 1491, 1562, 1564, 1581, 1605, 1660, 1670, 1704, 1716, 1724, 1815, 1869, 1880, 1912, 1947

Offset

1,1

Comments

The numbers x, y, z and t form an amicable quadruple according to Yanney's definition.

Links

Table of n, a(n) for n=1..53.

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Benjamin Franklin Yanney, Another definition of amicable numbers and some of their relations to Dickson's amicables, Amer. Math. Monthly, Vol. 30, No. 6 (1923), 311-315.

Example

114 is in the sequence since sigma(114) = sigma(158) = sigma(209) = sigma(239) = 240 = (114 + 158 + 209 + 239)/3.

Prog

(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

Crossrefs

Cf. A000203, A036471, A386726.

Sequence in context: A144413 A033811 A062446 * A053208 A355024 A338706

Adjacent sequences: A386724 A386725 A386726 * A386728 A386729 A386730

Keyword

nonn

Author

S. I. Dimitrov, Jul 31 2025

Extensions

More terms from Michel Marcus, Aug 01 2025

Status

approved