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 A181968 #31 Apr 21 2025 13:22:57
%S A181968 53,431,1457,3455,6749,11663,18521,27647,39365,53999,71873,93311,
%T A181968 118637,148175,182249,221183,265301,314927,370385,431999,500093,
%U A181968 574991,657017,746495,843749,949103,1062881,1185407,1317005,1457999,1608713,1769471,1940597,2122415
%N A181968 a(n) = 54n^3 - 1.
%C A181968 a(n) is coprime to 27*n^3*(27*n^3 - 1) - 2 = A016767(n)*(A016767(n)-1) - 2.
%C A181968 x^3 + y^3 + z^3 = w^3 has infinitely many solutions, where every pair of elements x, y and z are coprime.
%C A181968 This follows from the identity a(n)^3 + (A016767(n)+1)^3 + (A016768(n)-A008588(n))^3 = (A016768(n)+A008585(n))^3 for n >= 1.
%D A181968 Wacław Sierpiński, Czym sie zajmuje teoria liczb. Warsaw: PW "Wiedza Powszechna", 1957, pp. 59-60.
%H A181968 Arkadiusz Wesolowski, <a href="/A181968/b181968.txt">Table of n, a(n) for n = 1..1000</a>
%H A181968 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A181968 For n >= 1, a(n) = 54*A000578(n) - 1 = 2*A016767(n) - 1.
%F A181968 G.f.: (-1 + 57*x + 213*x^2 + 55*x^3)/(1 - x)^4.
%p A181968 seq(54*n^3-1, n=1..34);
%t A181968 Table[54*n^3 - 1, {n, 34}]
%o A181968 (Magma) [ 54*n^3-1 : n in [1..34]];
%o A181968 (PARI) vector(34, n, 54*n^3-1)
%Y A181968 Cf. A008585, A016767.
%K A181968 easy,nonn
%O A181968 1,1
%A A181968 _Arkadiusz Wesolowski_, Apr 06 2012