A068956 Number of distinct prime factors of n^n - (n-1)^(n-1).

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

Offset

2,4

Links

Table of n, a(n) for n=2..86.

Formula

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

Example

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

Mathematica

Table[ Length[ FactorInteger[n^n - (n - 1)^(n - 1)]], {n, 2, 52}] (* Reinhard Zumkeller *)
PrimeNu[#]&/@(#[[2]]-#[[1]]&/@Partition[Table[n^n, {n, 52}], 2, 1] (* Harvey P. Dale, Aug 24 2014 *)

Crossrefs

Cf. A001221, A007781, A068957.

Sequence in context: A117919 A309106 A160014 * A124842 A134399 A094436

Adjacent sequences: A068953 A068954 A068955 * A068957 A068958 A068959

Keyword

nonn

Author

Reinhard Zumkeller, Mar 11 2002

Extensions

Edited and extended by Robert G. Wilson v, Mar 15 2002

a(53)-a(54) from Alois P. Heinz, May 12 2017

a(55)-a(86) from Amiram Eldar, Feb 06 2020

Status

approved