A274518 Numbers k such that k^2 divides A000073(k).

1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848, 80995824, 1300820976

Offset: 1

Author

Seiichi Manyama, Jun 26 2016

Keywords

• nonn
• more

Examples

			tribonacci(103) = 331800673921785084815380861 = 103^2 * 31275395788649739354829.
		

Crossrefs

Cf. A000073, A232570.

Programs

Ruby

require 'matrix'
def power(a, n, mod)
  return Matrix.I(a.row_size) if n == 0
  m = power(a, n >> 1, mod)
  m = (m * m).map{|i| i % mod}
  return m if n & 1 == 0
  (m * a).map{|i| i % mod}
end
def f(m, n, mod)
  ary0 = Array.new(m, 0)
  ary0[0] = 1
  v = Vector.elements(ary0)
  ary1 = [Array.new(m, 1)]
  (0..m - 2).each{|i|
    ary2 = Array.new(m, 0)
    ary2[i] = 1
    ary1 << ary2
  }
  a = Matrix[*ary1]
  (power(a, n, mod) * v)[m - 1]
end
p (1..10 ** 6).select{|i| f(3, i, i * i) == 0}

Extensions

a(9)-a(13) from Chai Wah Wu, Jan 29 2018