A174280 Smallest k such that tau(Fibonacci(k)) = tau(Fibonacci(n+k)).

1, 3, 4, 3, 9, 5, 4, 3, 4, 3, 8, 5, 4, 3, 19, 6, 9, 5, 4, 3, 10, 7, 8, 5, 4, 3, 14, 6, 33, 13, 10, 9, 8, 13, 6, 7, 18, 5, 4, 3, 21, 5, 4, 3, 8, 16, 6, 31, 10, 9, 8, 9, 6, 19, 6, 18, 14, 27, 14, 19, 10, 9, 8, 9, 6, 16, 6, 26, 10, 9, 8, 11, 6, 42, 14, 7, 20, 5, 4, 3

Offset

1,2

Comments

tau(n) is the number of divisors of n (A000005).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1284

Eric Weisstein's World of Mathematics, Divisor Function.

Example

a(2) = 3 because tau(Fibonacci(3)) = tau(2) = 2, tau(Fibonacci(3+2)) = tau(5) = 2.

Maple

with(numtheory) ;
with(combinat) ;
A174280 := proc(n)
        for k from 1 do
                if tau(fibonacci(k)) = tau(fibonacci(n+k)) then
                        return k;
                end if;
        end do:
end proc:
seq(A174280(n), n=1..80) ; # R. J. Mathar, Jul 06 2012

Mathematica

Table[k = 1; While[DivisorSigma[0, Fibonacci[k]] != DivisorSigma[0, Fibonacci[k + n]], k++]; k, {n, 100}] (* T. D. Noe, Mar 18 2013 *)

Crossrefs

Cf. A063375.

Sequence in context: A015887 A158134 A184853 * A172004 A051508 A281230

Adjacent sequences: A174277 A174278 A174279 * A174281 A174282 A174283

Keyword

nonn

Author

Michel Lagneau, Mar 15 2010

Status

approved