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 A067411 #42 Feb 20 2024 13:22:57 %S A067411 1,4,24,144,864,5184,31104,186624,1119744,6718464,40310784,241864704, %T A067411 1451188224,8707129344,52242776064,313456656384,1880739938304, %U A067411 11284439629824,67706637778944,406239826673664 %N A067411 Third column of triangle A067410 and second column of A067417. %C A067411 Let f(k) be the sum of the smallest three positive divisors of k, g(k) be the sum of the largest two positive divisors of k, this sequence from a(2) onwards contains the numbers k for which g(k) is a positive integer power of f(k). - _Yifan Xie_, Jan 27 2024 %H A067411 Vincenzo Librandi, <a href="/A067411/b067411.txt">Table of n, a(n) for n = 0..1000</a> %H A067411 Paul Barry and A. Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Barry2/barry94r.html">The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences</a>, J. Int. Seq. 13 (2010) # 10.8.2, Example 14. %H A067411 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a> %H A067411 Craig Knecht, <a href="/A067411/a067411.png">Number of tilings for a stackable six sphinx tile shape.</a> %H A067411 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (6). %F A067411 a(n) = A067410(n+2, 2) = A067417(n+1, 1). %F A067411 a(n) = 4 * 6^(n-1), for n >= 1, a(0)=1. %F A067411 G.f.: (1-2*x)/(1-6*x). %F A067411 E.g.f.: (2*exp(6*x)+1) / 3 = exp(3*x)*(cosh(3*x) + sinh(3*x)/3). - _Paul Barry_, Nov 20 2003 %F A067411 a(n) = Sum_{k=0..n} C(n,k) * A001045(n+k+1). - _Paul Barry_, Apr 19 2010 %t A067411 CoefficientList[Series[(1-2x)/(1-6x),{x,0,30}],x] (* _Harvey P. Dale_, Feb 26 2015 *) %o A067411 (PARI) a(n) = if(n<=0, 0, 4*6^(n-1) ); \\ _Joerg Arndt_, Feb 23 2014 %Y A067411 A002001, A067412 (second and fourth column of A067410), A000244, A067403 (first and third column of A067417), A000400 (powers of 6). %Y A067411 Row sums of A038195. %K A067411 nonn,easy %O A067411 0,2 %A A067411 _Wolfdieter Lang_, Jan 25 2002 %E A067411 Incorrect formula deleted by _Harvey P. Dale_, Feb 26 2015 %E A067411 Formula restored by _Sean A. Irvine_, Jan 10 2021