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 A059387 #38 Jan 10 2025 10:10:11
%S A059387 0,2,24,182,1200,7502,45864,277622,1672800,10057502,60406104,
%T A059387 362617862,2176246800,13059091502,78359364744,470170602902,
%U A059387 2821066795200,16926530173502,101559568985784,609358577224742,3656154952230000
%N A059387 Jordan function J_n(6) (see A059379).
%C A059387 a(n) = A000225(n) * A024023(n) = (2^n - 1) * (3^n - 1) . a(n) is the number of n-tuples of elements e_1,e_2,...,e_n in the cyclic group C_6 such that the subgroup generated by e_1,e_2,...,e_n is C_6. - Sharon Sela (sharonsela(AT)hotmail.com), Jun 02 2002
%C A059387 Szalay proves that this sequence contains no squares except for 0. He & Liu prove that this sequence contains no higher powers aside from 2. - _Charles R Greathouse IV_, Jan 10 2025
%D A059387 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%H A059387 Vincenzo Librandi, <a href="/A059387/b059387.txt">Table of n, a(n) for n = 0..300</a>
%H A059387 Bo He and Chang Liu, <a href="https://arxiv.org/abs/2501.04050">The diophantine equation (2^k-1)*(3^k-1)=x^n</a>, arXiv preprint (2025). arXiv:2501.04050 [math.NT].
%H A059387 L. Szalay, <a href="https://web.archive.org/web/20221201120224id_/https://publi.math.unideb.hu/load_doi.php?pdoi=10_5486_PMD_2000_2069">On the Diophantine equation (2n - 1)(3n - 1) = x^2, Publicationes Mathematicae Debrecen, 57(1-2) (2000), pp. 1-9.
%H A059387 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).
%F A059387 G.f.: -2*x*(6*x^2-1) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). - _Colin Barker_, Dec 06 2012
%F A059387 a(n-1) = (limit of (Sum_{k>=0} (1/(6*k + 1)^s - 1/(6*k + 2)^s - 2/(6*k + 3)^s - 1/(6*k + 4)^s + 1/(6*k + 5)^s + 2/(6*k + 6)^s) as s -> n))/zeta(n)*6^(n - 1). - _Mats Granvik_, Nov 14 2013
%F A059387 a(n) = 2*A160869(n). - _R. J. Mathar_, Nov 23 2018
%p A059387 A059387:=n->(2^n-1)*(3^n-1); seq(A059387(n), n=0..50); # _Wesley Ivan Hurt_, Nov 14 2013
%t A059387 Table[(2^n-1)*(3^n-1),{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010 *)
%o A059387 (Magma) [(2^n-1)*(3^n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 05 2011
%o A059387 (PARI) for(n=0,30, print1((2^n-1)*(3^n-1), ", ")) \\ _G. C. Greubel_, Jan 29 2018
%Y A059387 Cf. A000225, A024023.
%K A059387 nonn,easy
%O A059387 0,2
%A A059387 _N. J. A. Sloane_, Jan 29 2001