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

0,2

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) = 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

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

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

Row sums of A038195.

Sequence in context: A114169 A121102 A307526 * A045915 A052609 A077613

Adjacent sequences: A067408 A067409 A067410 * A067412 A067413 A067414

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