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 A365806 #7 Oct 01 2023 11:17:26 %S A365806 1,2,8,27,32,45,99,108,128,135,180,369,396,432,512,540,567,675,720, %T A365806 855,1287,1476,1584,1728,2048,2160,2205,2268,2673,2700,2880,3420,5148, %U A365806 5445,5904,6336,6912,7803,8073,8192,8640,8820,9072,9477,10125,10647,10692,10800,11520,13680,17325,18513,20592,21780,23616,25344 %N A365806 Numbers k such that A243071(k) is a square. %C A365806 Sequence A163511(n^2), n >= 0, sorted into ascending order. %C A365806 Contains no squares after the initial 1. See A365808 for a proof. %C A365806 Question: Are there any more odd cubes or odd powers after 1, 27, 35937 ? %o A365806 (PARI) %o A365806 A243071(n) = if(n<=2, n-1, my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p*p2*(2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); ((3<<#binary(res\2))-res-1)); \\ (Combining programs given in A156552 and A054429) %o A365806 isA365806(n) = issquare(A243071(n)); %Y A365806 Cf. A000290, A004171 (subsequence), A010052, A163511, A243071, A365808. %K A365806 nonn %O A365806 1,2 %A A365806 _Antti Karttunen_, Oct 01 2023