cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: S. I. Dimitrov

S. I. Dimitrov's wiki page.

S. I. Dimitrov has authored 36 sequences. Here are the ten most recent ones:

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

Views

Author

S. I. Dimitrov, Aug 25 2025

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

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

Views

Author

S. I. Dimitrov, Aug 25 2025

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

A386933 Integers z such that there exist two integers 0

Original entry on oeis.org

81900, 161700, 163800, 175350, 245700, 261660, 323400, 327600, 350700, 409500, 485100, 490770, 491400, 499380, 523320, 526050, 526260, 573300, 646800, 647010, 655200, 671370, 701400, 702450, 737100, 784980, 808500, 819000, 876750, 970200, 971880, 981540, 982800, 990150, 998760
Offset: 1

Views

Author

S. I. Dimitrov, Aug 09 2025

Keywords

Comments

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

Examples

			163800 is in the sequence since psi(158340) = psi(161700) = psi(163800) = 564480 = 158340 + 161700 + 163800. Other examples: (322140, 322140, 323400), (14127960, 14224980, 14224980).

Links

Crossrefs

Cf. A001615, A125492, A323330, A385852, A386901.

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

Views

Author

S. I. Dimitrov, Aug 07 2025

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

A385852 Integers x such that there exist two integers 0

Original entry on oeis.org

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

Views

Author

S. I. Dimitrov, Aug 07 2025

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

A386727 Numbers x such that there exist three integers 0

Original entry on oeis.org

3, 10, 24, 51, 78, 105, 114, 136, 186, 220, 224, 255, 322, 348, 357, 370, 435, 478, 506, 616, 642, 710, 748, 820, 861, 885, 957, 996, 1004, 1068, 1113, 1214, 1221, 1276, 1292, 1336, 1390, 1485, 1491, 1562, 1564, 1581, 1605, 1660, 1670, 1704, 1716, 1724, 1815, 1869, 1880, 1912, 1947
Offset: 1

Views

Author

S. I. Dimitrov, Jul 31 2025

Keywords

Comments

The numbers x, y, z and t form an amicable quadruple according to Yanney’s definition.

Examples

			114 is in the sequence since sigma(114) = sigma(158) = sigma(209) = sigma(239) = 240 = (114 + 158 + 209 + 239)/3.

Links

Crossrefs

Cf. A000203, A036471, A386726.

Programs

  • PARI
    isok(x1) = my(s=sigma(x1), vx=select(x->(x>=x1), invsigma(s)), v=vector(4, i, vx[1])); for (i=1, #vx, v[2] = vx[i]; for (j=1, #vx, v[3] = vx[j]; for (k=1, #vx, v[4] = vx[k]; if (vecsum(v) == 3*s, return(1));););); \\ Michel Marcus, Aug 01 2025

Extensions

More terms from Michel Marcus, Aug 01 2025

A386726 Numbers x such that there exist two integers 0

Original entry on oeis.org

2, 238, 280, 308, 310, 382, 790, 795, 920, 952, 1034, 1162, 1246, 1330, 1410, 1434, 2002, 2024, 2506, 2632, 2728, 2750, 2926, 3040, 3210, 3452, 3496, 3500, 3630, 4134, 4260, 4466, 4550, 4968, 5080, 5278, 5396, 5520, 5530, 5756, 6128, 6230, 6426, 6888, 7288, 7584, 7640, 7910, 7990
Offset: 1

Views

Author

S. I. Dimitrov, Jul 31 2025

Keywords

Comments

The numbers x, y and z form an amicable triple according to Yanney's definition.

Examples

			238 is in the sequence since sigma(238) = sigma(255) = sigma(371) = 432 = (238 + 255 + 371)/2.

Links

Crossrefs

Cf. A000203, A125490, A386727.

Programs

  • PARI
    isok(x1) = my(s=sigma(x1), vx=select(x->(x>=x1), invsigma(s)), v=vector(3, i, vx[1])); for (i=1, #vx, v[2] = vx[i]; for (j=1, #vx, v[3] = vx[j]; if (vecsum(v) == 2*s, return(1)););); \\ Michel Marcus, Aug 01 2025

Extensions

More terms from Michel Marcus, Aug 01 2025

A386672 Integers x such that there exist four integers 0

Original entry on oeis.org

46, 94, 946, 1139, 1680, 3804, 4200, 29975, 31143, 48560, 53428, 63840, 74178, 121400, 125280, 135720, 279300, 483392, 679952
Offset: 1

Views

Author

S. I. Dimitrov, Jul 28 2025

Keywords

Comments

The numbers x, y, z, t and w form a sigma-quintic quintuple.
Other terms of the sequence: 5446350, 20201728, 326481408.

Examples

			(46, 19, 43, 47, 67) is such a quintuple because sigma(46)^5 = 72^5 = 46^5 + 19^5 + 43^5 + 47^5 + 67^5.
Other examples: (94, 38, 86, 92, 134), (946, 418, 1012, 1034, 1474), (1139, 323, 731, 782, 799), (63840, 144480, 154560, 157920, 225120).

Links

Crossrefs

Cf. A000203, A003350, A063922, A386225.

Extensions

More terms from Michel Marcus, Jul 29 2025

A386225 Numbers x such that there exist four integers 00, t>0 and w>0 such that sigma(x)^4 = sigma(y)^4 = x^4 + y^4 + z^4 + t^4 + w^4.

Original entry on oeis.org

24, 240, 600
Offset: 1

Views

Author

S. I. Dimitrov, Jul 15 2025

Keywords

Comments

The numbers x, y, z, t and w form a sigma-quartic quintuple.
[91963648, 91963648, 137945472, 183927296, 183927296] is another quintuple. - Michel Marcus, Jul 28 2025

Examples

			(24, 24, 36, 48, 48) is such a quintuple because sigma(24)^4 = sigma(24)^4 = 60^4 = 24^4 + 24^4 + 36^4 + 48^4 + 48^4.
(240, 240, 240, 408, 720) and (600, 600, 600, 1020, 1800) are the two next quintuples.

Links

Crossrefs

Cf. A000203, A003339, A297305, A385397.

Programs

  • PARI
    find4(ss) = my(v=List(), k, t); ss\=1; for(x=1, sqrtnint(ss-2, 4), for(y=1, min(sqrtnint(ss-x^4-1, 4), x), k=x^4+y^4; for(z=1, min(sqrtnint(ss-k, 4), y), if (k+z^4==ss, return([x,y,z])))));
isok4(x) = my(s=sigma(x), v=select(z->(z>=x), invsigma(s))); if (#v >=2, for (i=1, #v, my(k=s^4 - x^4 - v[i]^4); if (k>0, my(xyz = find4(k)); if (xyz, return([x, v[i], xyz[1], xyz[2], xyz[3]]));););); \\ Michel Marcus, Jul 22 2025

A386378 Integers x such that there exist four integers 00 and w>0 such that sigma(x)^3 = sigma(y)^3 = sigma(z)^3 = x^3 + y^3 + z^3 + t^3 + w^3.

Original entry on oeis.org

30, 62, 90, 174, 238, 357, 390, 440, 495, 552, 762, 870, 894, 924, 1056, 1146, 1248, 1386, 1560, 1740, 1770, 1782, 1824, 1880, 1938, 1992, 2046, 2208, 2262, 2472, 2568, 2625, 2670, 2686, 2730, 2840, 2856, 3000, 3190, 3382, 3630, 3666, 3720, 3738, 3828, 3885, 3960, 3984
Offset: 1

Views

Author

S. I. Dimitrov, Jul 20 2025

Keywords

Comments

The numbers x, y, z, t and w form a sigma-cubic quintuple. See Dimitrov link.

Examples

			(174, 190, 323, 5, 94) is such a quintuple because sigma(174)^3 = sigma(190)^3 = sigma(323)^3 = 360^3 = 174^3 + 190^3 + 323^3 + 5^3 + 94^3.

Links

Crossrefs

Cf. A000203, A003325, A003328, A385325, A385397.

Programs

  • PARI
    is23(n) = my(z); for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3, &z) && return([k,z]));
isok3(x) = my(s=sigma(x), v=select(z->(z>=x), invsigma(s))); if (#v >= 1, for (i=1, #v, for (j=1, #v, my(k=s^3 - x^3 - v[i]^3-v[j]^3); if (k>0, my(tw = is23(k)); if (tw, return([x, v[i], v[j], tw[1], tw[2]])););););); \\ Michel Marcus, Jul 22 2025

Extensions

Corrected and extended by Michel Marcus, Jul 22 2025

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