A377032 Odd numbers k such that A000045(k)/A000005(k) is an integer.

1, 3, 405, 625, 1875, 50625, 354375, 556875, 658125, 860625, 961875, 1164375, 1468125, 1500625, 1569375, 1873125, 2075625, 2176875, 2379375, 2683125, 2986875, 3088125, 3391875, 3594375, 3695625, 3720087, 3999375, 4201875, 4501875, 4505625, 4910625, 5113125, 5214375, 5416875, 5518125, 5720625

Offset

1,2

Comments

Odd numbers k such that Fibonacci(k) is divisible by tau(k).

Includes 15^4 * p for primes p > 5.

Links

Robert Israel, Table of n, a(n) for n = 1..250

Example

a(3) = 405 is a term because 405 = 3^4 * 5 is odd, tau(405) = 10, and Fibonacci(405) = 1952132532477489958194625524584538730388053593825001030592563956919572392152809678530 is divisible by 10.

Maple

filter:= proc(n) uses LinearAlgebra:-Modular; local t, Mt, dt;
  t:= numtheory:-tau(n);
  if t < 2^25 then Mt:= Mod(t, M, float[8]) else Mt:= Mod(t, M, integer) fi;;
  MatrixPower(t, M, n)[1, 2] = 0
end proc:
filter(1):= true:
select(filter, [seq(i, i=1..600000, 2)]);

Crossrefs

Intersection of A160684 and A005408.

Sequence in context: A203563 A181990 A198666 * A330014 A305664 A152517

Adjacent sequences: A377029 A377030 A377031 * A377033 A377034 A377035

Keyword

nonn

Author

Robert Israel, Oct 14 2024

Status

approved