A386933 -id:A386933 - cp's OEIS frontend

A385852 Integers x such that there exist two integers 0

79170, 150150, 158340, 161070, 232050, 237510, 300300, 316680, 322140, 395850, 450450, 464100, 468930, 474810, 475020, 483210, 554190, 570570, 600600, 622440, 633360, 641550, 644280, 696150, 712530, 750750, 791700, 805350, 937860, 949620, 950040, 963270, 966420

Offset: 1

S. I. Dimitrov, Aug 07 2025

The numbers x, y and z form a psi-amicable triple according to Dimitrov's definition.

			79170 is in the sequence since psi(79170) = psi(80850) = psi(81900) = 241920 = 79170 + 80850 + 81900. Other examples: (161070, 161070, 161700), (7063980, 7112490, 7112490).

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

Cf. A001615, A125490, A323329, A386901, A386933.

A386901 Integers y such that there exist two integers 0

Original entry on oeis.org

80850, 158340, 161070, 161700, 232050, 242550, 316680, 322140, 323400, 404250, 464100, 474810, 475020, 483210, 485100, 485940, 565950, 633360, 641550, 644280, 646800, 662340, 696150, 727650, 791700, 805350, 808500, 963270, 966420, 967890, 970200, 971880

Offset: 1

S. I. Dimitrov, Aug 07 2025

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

			158340 is in the sequence since psi(150150) = psi(158340) = psi(175350) = 483840 = 150150 + 158340 + 175350. Other examples: (232050, 232050, 261660), (7091700, 7098630, 7098630).

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

Cf. A001615, A125491, A323329, A385852, A386933.

A387290 Numbers k such that there exist three numbers x, y and z such that k = psi(x) = psi(y) = psi(z) = x + y + z.

Original entry on oeis.org

241920, 483840, 725760, 967680, 1209600, 1451520, 1693440, 1935360, 2177280, 2419200, 2903040, 3386880, 3628800, 3870720, 4354560, 4838400, 5080320, 5253120, 5806080, 6048000, 6531840, 6773760, 6967296, 7257600, 7741440, 7879680, 8467200, 8709120, 9123840, 9676800

Offset: 1

S. I. Dimitrov, Aug 25 2025

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

			241920 is in the sequence since 241920 = psi(79170) = psi(80850) = psi(81900) = 79170 + 80850 + 81900.

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

Cf. A001615, A137231, A385852, A386901, A386933.

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.

Original entry on oeis.org

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.

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A385852 Integers x such that there exist two integers 0

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A386901 Integers y such that there exist two integers 0

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A387290 Numbers k such that there exist three numbers x, y and z such that k = psi(x) = psi(y) = psi(z) = x + y + z.

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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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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.

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