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

%I A274518 #20 Jul 15 2023 14:12:21
%S A274518 1,103,112,2621,30576,77168,694512,9919728,24770928,55638128,57268848,
%T A274518 80995824,1300820976
%N A274518 Numbers k such that k^2 divides A000073(k).
%e A274518 tribonacci(103) = 331800673921785084815380861 = 103^2 * 31275395788649739354829.
%o A274518 (Ruby)
%o A274518 require 'matrix'
%o A274518 def power(a, n, mod)
%o A274518   return Matrix.I(a.row_size) if n == 0
%o A274518   m = power(a, n >> 1, mod)
%o A274518   m = (m * m).map{|i| i % mod}
%o A274518   return m if n & 1 == 0
%o A274518   (m * a).map{|i| i % mod}
%o A274518 end
%o A274518 def f(m, n, mod)
%o A274518   ary0 = Array.new(m, 0)
%o A274518   ary0[0] = 1
%o A274518   v = Vector.elements(ary0)
%o A274518   ary1 = [Array.new(m, 1)]
%o A274518   (0..m - 2).each{|i|
%o A274518     ary2 = Array.new(m, 0)
%o A274518     ary2[i] = 1
%o A274518     ary1 << ary2
%o A274518   }
%o A274518   a = Matrix[*ary1]
%o A274518   (power(a, n, mod) * v)[m - 1]
%o A274518 end
%o A274518 p (1..10 ** 6).select{|i| f(3, i, i * i) == 0}
%Y A274518 Cf. A000073, A232570.
%K A274518 nonn,more
%O A274518 1,2
%A A274518 _Seiichi Manyama_, Jun 26 2016
%E A274518 a(9)-a(13) from _Chai Wah Wu_, Jan 29 2018