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.

A383714 Integers k such that there exists an integer 0 such that m*sigma(m)^2 + k*sigma(k)^2 = (m+k)^3.

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%I A383714 #108 Jul 10 2025 12:14:32
%S A383714 21,231,284,1210,2499,2924,5564,6368,10856,14595,18416,66992,71145,
%T A383714 76084,87633,88730
%N A383714 Integers k such that there exists an integer 0<m<k such that m*sigma(m)^2 + k*sigma(k)^2 = (m+k)^3.
%C A383714 The numbers m and k form a WPM(2)-amicable pair (WPM = weighted power mean). See Dimitrov link.
%H A383714 S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024.
%e A383714 (7, 21) is such a pair because 7*sigma(7)^2 + 21*sigma(21)^2 = 7*8^2 + 21*32^2 = (7+21)^3.
%o A383714 (PARI) isok(k)= for (m=1, k-1, if (m*sigma(m)^2 + k*sigma(k)^2 == (m+k)^3, return(m))); \\ _Michel Marcus_, May 15 2025
%Y A383714 Cf. A002046 (a subsequence), A063990, A259180, A383239, A383483, A383484.
%K A383714 nonn,more
%O A383714 1,1
%A A383714 _S. I. Dimitrov_, May 14 2025
%E A383714 a(3)-a(16) from _Michel Marcus_, May 15 2025