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.

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

Author

S. I. Dimitrov, Aug 25 2025

Keywords

• nonn
• easy
• new

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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