A067411 Third column of triangle A067410 and second column of A067417.

1, 4, 24, 144, 864, 5184, 31104, 186624, 1119744, 6718464, 40310784, 241864704, 1451188224, 8707129344, 52242776064, 313456656384, 1880739938304, 11284439629824, 67706637778944, 406239826673664

Offset: 0

Author

Wolfdieter Lang, Jan 25 2002

Keywords

• nonn
• easy

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).

Crossrefs

A002001, A067412 (second and fourth column of A067410), A000244, A067403 (first and third column of A067417), A000400 (powers of 6).

Row sums of A038195.

Programs

Mathematica

CoefficientList[Series[(1-2x)/(1-6x),{x,0,30}],x] (* Harvey P. Dale, Feb 26 2015 *)

PARI

a(n) = if(n<=0, 0, 4*6^(n-1) ); \\ Joerg Arndt, Feb 23 2014

Formula

a(n) = A067410(n+2, 2) = A067417(n+1, 1).

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

Extensions

Incorrect formula deleted by Harvey P. Dale, Feb 26 2015

Formula restored by Sean A. Irvine, Jan 10 2021