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 1-1 of 1 results.

A384255 Integers k such that there exists an integer 0

Original entry on oeis.org

2, 21, 27, 123, 175, 2133, 2187, 6093, 340917, 504309, 1594323, 1895841, 5308415, 23006577, 62188641
Offset: 1

Views

Author

S. I. Dimitrov, May 23 2025

Keywords

Comments

The most interesting question that arises here is whether there exist such pairs for which sigma(m) = sigma(k), which would imply that sigma(m)^2 = sigma(k)^2 = m^2+k^2. None have been found for m < k <= 10^8.

Examples

			(13, 21) is such a pair because sigma(13)^2 + sigma(21)^2 = 14^2 + 32^2 = 2*(13^2+21^2).

Links

Crossrefs

Cf. A063990, A259180, A383484, A383714

Programs

  • Mathematica
    f[n_]:=f[n]=DivisorSigma[1,n]^2-2*n^2;lst={};Do[AppendTo[lst,f@k];If[MemberQ[lst,-f@k],Print@k],{k,10000}] (* Giorgos Kalogeropoulos, May 29 2025 *)
  • PARI
    isok(k) = for(m=1, k-1, if (sigma(m)^2 + sigma(k)^2 == 2*(m^2+k^2), return(1))); \\ Michel Marcus, May 23 2025

Extensions

a(9)-a(15) from Giorgos Kalogeropoulos, May 29 2025
Showing 1-1 of 1 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.