A387486 -id:A387486 - cp's OEIS frontend

A387291 Integers x such that there exist two numbers y,z with x <= y <= z such that psi(x) = psi(y) = psi(z) = (x + y + z)/2.

2, 4, 6, 8, 16, 18, 28, 32, 44, 54, 64, 70, 105, 110, 128, 150, 162, 165, 182, 200, 238, 240, 256, 280, 310, 315, 364, 382, 468, 486, 512, 520, 585, 590, 644, 735, 750, 780, 790, 795, 800, 1000, 1024, 1034, 1162, 1246, 1260, 1274, 1410, 1434, 1456, 1458, 1472, 1540, 1575

Offset: 1

S. I. Dimitrov, Aug 25 2025

The numbers x, y and z form a psi-amicable triple.

			2 is in the sequence since psi(2) = 3 = (2 + 2 + 2)/2.
28 is in the sequence since psi(28) = psi(33) = psi(35) = 48 = (28 + 33 + 35)/2.

S. I. Dimitrov, On psi-amicable numbers and their generalizations, arXiv:2508.02318 [math.NT], 2025.

Cf. A001615, A385852, A386726, A386901, A386933, A387292, A387486.

mypsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
isok(k) = my(vk=invpsi(mypsi(k))); vk = select(x->x>=k, vk); if (#vk, my(x = 1); for (y=x, #vk, for (z=y, #vk, if (apsi(k) == (vk[x]+vk[y]+vk[z])/2, return(1););););); \\ Michel Marcus, Sep 04 2025

A387292 Integers x such that there exist three numbers y,z,and t with x<=y<=z<=t such that psi(x) = psi(y) = psi(z) = psi(t) = (x + y + z + t)/3.

Original entry on oeis.org

3, 4, 6, 8, 9, 10, 12, 27, 30, 32, 44, 45, 51, 52, 68, 75, 81, 96, 99, 100, 105, 112, 114, 152, 164, 171, 186, 188, 190, 192, 204, 225, 230, 238, 243, 246, 255, 260, 272, 284, 304, 308, 316, 322, 340, 342, 348, 352, 354, 357, 360, 370, 375, 380, 385, 396, 400, 406, 426, 430, 435, 441, 448, 456, 460, 464, 474, 476

Offset: 1

S. I. Dimitrov, Aug 25 2025

The numbers x, y, z and t form a psi-amicable quadruple according to Dimitrov's definition.

			44 is in the sequence since psi(44) = psi(46) = psi(55) = psi(71) = 72 = (44 + 46 + 55 + 71)/3.
45 is in the sequence since psi(45) = psi(45) = psi(55) = psi(71) = 72 = (45 + 45 + 55 + 71)/3.

S. I. Dimitrov, On psi-amicable numbers and their generalizations, arXiv:2508.02318 [math.NT], 2025.

Cf. A001615, A385852, A386727, A386901, A386933, A387291, A387486.

cp's OEIS Frontend

A387291 Integers x such that there exist two numbers y,z with x <= y <= z such that psi(x) = psi(y) = psi(z) = (x + y + z)/2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI