%I #24 Feb 06 2020 08:18:38

%S 1,1,1,2,2,1,3,6,3,1,3,2,3,3,2,1,2,3,3,2,2,3,3,4,7,4,2,2,5,4,5,3,6,4,

%T 4,2,4,7,6,4,3,4,7,6,2,7,4,7,10,6,4,5,5,7,7,5,5,6,2,5,8,4,6,5,5,3,5,4,

%U 4,2,3,4,8,4,6,4,5,7,5,13,8,4,2,5,6

%N Number of distinct prime factors of n^n - (n-1)^(n-1).

%F a(n) = A001221(A007781(n-1)).

%e A007781(13) = 10809131718965763 = 3 * 61^2 * 968299894201, therefore a(14) = 3.

%t Table[ Length[ FactorInteger[n^n - (n - 1)^(n - 1)]], {n, 2, 52}] (* _Reinhard Zumkeller_ *)

%t PrimeNu[#]&/@(#[[2]]-#[[1]]&/@Partition[Table[n^n,{n,52}],2,1] (* _Harvey P. Dale_, Aug 24 2014 *)

%Y Cf. A001221, A007781, A068957.

%K nonn

%O 2,4

%A _Reinhard Zumkeller_, Mar 11 2002

%E Edited and extended by _Robert G. Wilson v_, Mar 15 2002

%E a(53)-a(54) from _Alois P. Heinz_, May 12 2017

%E a(55)-a(86) from _Amiram Eldar_, Feb 06 2020