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

1,5

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.

Formula

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

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 *)

Prog

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

Crossrefs

Sequence in context: A068152 A278970 A182199 * A238352 A291357 A079636

Adjacent sequences: A217432 A217433 A217434 * A217436 A217437 A217438

Keyword

nonn,hard

Author

M. F. Hasler, Oct 02 2012

Extensions

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

Status

approved