A068956 - OEIS

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

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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 *)