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 A063680 #41 Jul 28 2025 06:15:44 %S A063680 74,531434,387420482,2541865828322 %N A063680 Solutions to sigma(k) + 7 = sigma(k+7). %C A063680 No other solutions < 4290000000. Sequence A063679 shows how to generate more solutions, but there may be solutions other than those produced by A063679. %C A063680 No others < 10^17. - _Seth A. Troisi_, Oct 25 2022 %C A063680 k or k+7 must be a square or twice a square (A028982). See comment in A015886. - _Seth A. Troisi_, Oct 26 2022 %C A063680 From _Jon E. Schoenfield_, Oct 26 2022: (Start) %C A063680 Each of the first 4 terms of the sequence is of the form k = 9^j - 7: %C A063680 74 = 9^2 - 7, %C A063680 531434 = 9^6 - 7, %C A063680 387420482 = 9^9 - 7, %C A063680 2541865828322 = 9^13 - 7. %C A063680 The next terms of this form are 9^53 - 7 and 9^82 - 7. %C A063680 Does the sequence contain any terms that are not of this form? %C A063680 (End) %C A063680 No other terms < 2.7*10^15. - _Jud McCranie_, Jul 27 2025 %e A063680 sigma(74) + 7 = 121 = sigma(74+7), so 74 is in the sequence. %o A063680 (PARI) isok(k) = sigma(k) + 7 == sigma(k+7); \\ _Michel Marcus_, Oct 25 2022 %Y A063680 Cf. A000203, A063679. %Y A063680 Cf. A054799, A015913, A015914, A015915, A015916, A015917, A054905. %K A063680 nonn,bref,hard,more %O A063680 1,1 %A A063680 _Jud McCranie_, Jul 28 2001 %E A063680 a(4) from _Seth A. Troisi_, Oct 24 2022