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.

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A385397 Numbers x such that there exist three integers 00 and w>0 such that sigma(x)^3 = sigma(y)^3 = x^3 + y^3 + z^3 + w^3.

Original entry on oeis.org

153, 216, 255, 324, 672, 735, 1074, 1170, 1218, 2430, 2655, 2736, 3482, 4148, 4605, 4935, 5220, 5446, 5916, 6048, 7140, 9340, 11000, 11160, 12768, 14090, 14098, 14980, 17220, 17696, 18984, 21068, 21948, 22128, 23022, 23205, 24297, 24570, 25284, 25740, 29058, 29640, 30240, 30690, 31008, 31190, 32760, 37140, 39840
Offset: 1

Views

Author

S. I. Dimitrov, Jun 27 2025

Keywords

Comments

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

Examples

			(255, 321, 84, 312) is such a quadruple because sigma(255)^3 = sigma(321)^3 = 432^3 = 255^3 + 321^3 + 84^3 + 312^3.

Links

Crossrefs

Cf. A000203, A385325, A385356.

Programs

  • PARI
    issc(n) = if (n>0, for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1))); \\ A003325
isok(x) = my(s=sigma(x)); for (y=1, x, if (s == sigma(y), if (issc(s^3-x^3-y^3), return(1)););); \\ Michel Marcus, Jun 27 2025

Extensions

More terms from David A. Corneth, Jun 27 2025

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
Showing 1-2 of 2 results.

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