A385325 Numbers x such that there exist two integers y, z both >0 such that sigma(x)^3 = x^3 + y^3 + z^3.

5, 6, 53, 58, 102, 118, 152, 168, 197, 214, 250, 258, 408, 426, 445, 476, 487, 491, 508, 672, 760, 783, 861, 885, 1182, 1204, 1242, 1299, 1305, 1350, 1615, 1890, 1988, 1992, 2040, 2082, 2190, 2465, 2519, 2679, 3105, 3144, 3213, 3276, 3292, 3432, 3994, 4035, 4210, 4256

Offset: 1

Author

S. I. Dimitrov, Jun 25 2025

Keywords

• nonn

Comments

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

If sigma(x)^3 = x^3 + y^3 + z^3 then sigma(x)^3 - x^3 = y^3 + z^3 = (y + z)*(y^2 - y*z + z^2) which enables comparing pairwise divisors of sigma(x)^3 - x^3 to see if sigma(x)^3 - x^3 is the sum of two cubes. - David A. Corneth, Jun 26 2025

Examples

			(3, 4, 5) is such a triple because sigma(5)^3 = 6^3 = 5^3 + 4^3 + 3^3.
6 is in the sequence as sigma(6)^3 = 6^3 + 8^3 + 10^3. - _David A. Corneth_, Jun 26 2025
		

Links

• David A. Corneth, PARI program
• S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Crossrefs

Cf. A000203, A003325, A066784, A096545.

Programs

PARI

\\ See Corneth link

Extensions

Data corrected by David A. Corneth, Jun 26 2025