A386726 Numbers x such that there exist two integers 0<x<=y<=z such that sigma(x) = sigma(y) = sigma(z) = (x + y + z)/2.

2, 238, 280, 308, 310, 382, 790, 795, 920, 952, 1034, 1162, 1246, 1330, 1410, 1434, 2002, 2024, 2506, 2632, 2728, 2750, 2926, 3040, 3210, 3452, 3496, 3500, 3630, 4134, 4260, 4466, 4550, 4968, 5080, 5278, 5396, 5520, 5530, 5756, 6128, 6230, 6426, 6888, 7288, 7584, 7640, 7910, 7990

Offset

1,1

Comments

The numbers x, y and z form an amicable triple according to Yanney's definition.

Links

Table of n, a(n) for n=1..49.

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

238 is in the sequence since sigma(238) = sigma(255) = sigma(371) = 432 = (238 + 255 + 371)/2.

Prog

(PARI) isok(x1) = my(s=sigma(x1), vx=select(x->(x>=x1), invsigma(s)), v=vector(3, i, vx[1])); for (i=1, #vx, v[2] = vx[i]; for (j=1, #vx, v[3] = vx[j]; if (vecsum(v) == 2*s, return(1)); ); ); \\ Michel Marcus, Aug 01 2025

Crossrefs

Cf. A000203, A125490, A386727.

Sequence in context: A139963 A124046 A101146 * A159280 A013477 A013473

Adjacent sequences: A386723 A386724 A386725 * A386727 A386728 A386729

Keyword

nonn

Author

S. I. Dimitrov, Jul 31 2025

Extensions

More terms from Michel Marcus, Aug 01 2025

Status

approved