A387486 Numbers x such that there exist four integers y, z, t and w with x<=y<=z<=t<=w such that psi(x) = psi(y) = psi(z) = psi(t) = psi(w) = (x + y + z + t + w)/4.

4, 6, 8, 12, 28, 30, 32, 36, 40, 44, 45, 78, 84, 98, 104, 112, 124, 140, 158, 174, 176, 180, 192, 196, 198, 200, 204, 216, 220, 225, 230, 232, 236, 238, 254, 260, 272, 276, 284, 300, 304, 310, 320, 332, 340, 342, 348, 350, 354, 357, 360, 364, 368, 374, 378, 380

Offset: 1

Author

S. I. Dimitrov, Aug 31 2025

Keywords

• nonn
• easy
• new

Comments

The numbers x, y, z, t and w form a psi-amicable quintuple.

Examples

			200 is in the sequence since psi(200) = psi(267) = psi(295) = psi(319) = psi(359) = 360 = (200 + 267 + 295 + 319 + 359)/4.
		

Links

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

Crossrefs

Cf. A001615, A385852, A387291, A387292.