A217435 Number of prime factors of n^n+(n-1)^(n-1), counted with multiplicity.

1, 1, 1, 1, 4, 2, 3, 2, 3, 2, 5, 2, 6, 4, 2, 3, 6, 3, 3, 4, 6, 2, 7, 3, 5, 5, 3, 3, 5, 3, 3, 3, 7, 4, 5, 4, 3, 2, 2, 2, 6, 3, 6, 4, 5, 3, 8, 6, 6, 3, 5, 5, 5, 5, 3, 3, 5, 2, 8, 4, 4, 6, 6, 6, 8, 8, 4, 3, 4, 7, 7, 6, 6, 4, 4, 7, 9, 6, 7, 5, 9, 5, 7, 4, 3, 5, 6, 7, 9, 3, 2, 5

Offset: 1

Author

M. F. Hasler, Oct 02 2012

Keywords

• nonn
• hard

Links

• M. F. Hasler and Amiram Eldar, Table of n, a(n) for n = 1..143 (terms 1..112 from M. F. Hasler)
• W. Nissen, np ( n ) = n^n + (n+1)^(n+1) — 2 prominent questions, Oct 02 2012.
• W. Nissen, Prime factors of np ( n ) = n^n + (n+1)^(n+1), Up for the Count.

Programs

Maple

A217435:=n->numtheory[bigomega](n^n+(n-1)^(n-1)): seq(A217435(n), n=1..30); # Wesley Ivan Hurt, Jan 27 2017

Mathematica

Join[{1}, Table[PrimeOmega[n^n + (n-1)^(n-1)], {n, 2, 30}]] (* Amiram Eldar, Feb 24 2020 *)
Join[{1},PrimeOmega[Total/@Partition[#^#&/@Range[30],2,1]]] (* Harvey P. Dale, Oct 02 2021 *)

PARI

for(n=1,999,print1(bigomega((n-1)^(n-1)+n^n)","))

Formula

a(n) = A001222(A056788(n)).

Extensions

Data beyond a(49) from W. Nissen's web site.