A387292 -id:A387292 - 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

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.

Original entry on oeis.org

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

S. I. Dimitrov, Aug 31 2025

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

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

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

Cf. A001615, A385852, A387291, A387292.

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.

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