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.
%I A385325 #30 Jun 27 2025 10:54:55 %S A385325 5,6,53,58,102,118,152,168,197,214,250,258,408,426,445,476,487,491, %T A385325 508,672,760,783,861,885,1182,1204,1242,1299,1305,1350,1615,1890,1988, %U A385325 1992,2040,2082,2190,2465,2519,2679,3105,3144,3213,3276,3292,3432,3994,4035,4210,4256 %N A385325 Numbers x such that there exist two integers y, z both >0 such that sigma(x)^3 = x^3 + y^3 + z^3. %C A385325 The numbers x, y and z form a sigma-cubic triple. See Dimitrov link. %C A385325 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 %H A385325 David A. Corneth, <a href="/A385325/a385325.gp.txt">PARI program</a> %H A385325 S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024. %e A385325 (3, 4, 5) is such a triple because sigma(5)^3 = 6^3 = 5^3 + 4^3 + 3^3. %e A385325 6 is in the sequence as sigma(6)^3 = 6^3 + 8^3 + 10^3. - _David A. Corneth_, Jun 26 2025 %o A385325 (PARI) \\ See Corneth link %Y A385325 Cf. A000203, A003325, A066784, A096545. %K A385325 nonn %O A385325 1,1 %A A385325 _S. I. Dimitrov_, Jun 25 2025 %E A385325 Data corrected by _David A. Corneth_, Jun 26 2025