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.

Showing 1-3 of 3 results.

A385531 Numbers x such that there exist three integers 00 such that sigma(x)^2 = sigma(y)^2 = sigma(z)^2 = x^2 + y^2 + z^2 + t^2.

Original entry on oeis.org

4, 6, 28, 45, 48, 60, 156, 204, 208, 360, 496, 1170, 2016, 2520, 2925, 3480, 4796, 5532, 5733, 7152, 7605, 8128, 9680, 11050, 12402, 15776, 33468, 36720, 37064, 38408, 43584, 50960, 55216, 63708, 70364, 83772, 92280, 106700, 114840, 116288, 149400, 163800, 166617, 167580
Offset: 1

Views

Author

S. I. Dimitrov, Jul 02 2025

Keywords

Comments

The numbers x, y, z and t form a sigma-quadratic quadruple. See Dimitrov link.

Examples

			(3480, 3672, 4296, 8520) is such a quadruple because sigma(3480)^2 = sigma(3672)^2 = sigma(4296)^2 = 3480^2 + 3672^2 + 4296^2 + 8520^2.

Links

Crossrefs

Cf. A000203, A000414, A385356, A385397.

Programs

  • PARI
    isok(x) = my(s=sigma(x), vi=select(t->(t>=x), invsigma(s))); for (i=1, #vi, for (j=1, #vi, for (k=1, #vi, if ((i==1) || (j==1) || (k==1), my(ss = s^2 - vi[i]^2 - vi[j]^2 - vi[k]^2); if (ss && issquare(ss), return(1)););););); \\ Michel Marcus, Jul 09 2025
  • PARI
    \\ See Corneth link

Extensions

Some missing terms added by Michel Marcus, Jul 09 2025
More terms from David A. Corneth, Jul 09 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
Showing 1-3 of 3 results.

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