A174280 - OEIS

%I #28 Oct 12 2024 21:31:14

%S 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,

%T 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,

%U 19,10,9,8,9,6,16,6,26,10,9,8,11,6,42,14,7,20,5,4,3

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

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

%H Chai Wah Wu, <a href="/A174280/b174280.txt">Table of n, a(n) for n = 1..1284</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>.

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

%p with(numtheory) ;

%p with(combinat) ;

%p A174280 := proc(n)

%p         for k from 1 do

%p                 if tau(fibonacci(k)) = tau(fibonacci(n+k)) then

%p                         return k;

%p                 end if;

%p         end do:

%p end proc:

%p seq(A174280(n),n=1..80) ; # _R. J. Mathar_, Jul 06 2012

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

%Y Cf. A063375.

%K nonn

%O 1,2

%A _Michel Lagneau_, Mar 15 2010