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%I #42 Feb 20 2024 13:22:57
%S 1,4,24,144,864,5184,31104,186624,1119744,6718464,40310784,241864704,
%T 1451188224,8707129344,52242776064,313456656384,1880739938304,
%U 11284439629824,67706637778944,406239826673664
%N Third column of triangle A067410 and second column of A067417.
%C 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 Vincenzo Librandi, <a href="/A067411/b067411.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H Craig Knecht, <a href="/A067411/a067411.png">Number of tilings for a stackable six sphinx tile shape.</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (6).
%F a(n) = A067410(n+2, 2) = A067417(n+1, 1).
%F a(n) = 4 * 6^(n-1), for n >= 1, a(0)=1.
%F G.f.: (1-2*x)/(1-6*x).
%F 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 a(n) = Sum_{k=0..n} C(n,k) * A001045(n+k+1). - _Paul Barry_, Apr 19 2010
%t CoefficientList[Series[(1-2x)/(1-6x),{x,0,30}],x] (* _Harvey P. Dale_, Feb 26 2015 *)
%o (PARI) a(n) = if(n<=0, 0, 4*6^(n-1) ); \\ _Joerg Arndt_, Feb 23 2014
%Y A002001, A067412 (second and fourth column of A067410), A000244, A067403 (first and third column of A067417), A000400 (powers of 6).
%Y Row sums of A038195.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jan 25 2002
%E Incorrect formula deleted by _Harvey P. Dale_, Feb 26 2015
%E Formula restored by _Sean A. Irvine_, Jan 10 2021
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