OFFSET
0,2
COMMENTS
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
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Paul Barry and A. Hennessy, The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences, J. Int. Seq. 13 (2010) # 10.8.2, Example 14.
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Craig Knecht, Number of tilings for a stackable six sphinx tile shape.
Index entries for linear recurrences with constant coefficients, signature (6).
FORMULA
a(n) = 4 * 6^(n-1), for n >= 1, a(0)=1.
G.f.: (1-2*x)/(1-6*x).
E.g.f.: (2*exp(6*x)+1) / 3 = exp(3*x)*(cosh(3*x) + sinh(3*x)/3). - Paul Barry, Nov 20 2003
a(n) = Sum_{k=0..n} C(n,k) * A001045(n+k+1). - Paul Barry, Apr 19 2010
MATHEMATICA
CoefficientList[Series[(1-2x)/(1-6x), {x, 0, 30}], x] (* Harvey P. Dale, Feb 26 2015 *)
PROG
(PARI) a(n) = if(n<=0, 0, 4*6^(n-1) ); \\ Joerg Arndt, Feb 23 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 25 2002
EXTENSIONS
Incorrect formula deleted by Harvey P. Dale, Feb 26 2015
Formula restored by Sean A. Irvine, Jan 10 2021
STATUS
approved