A078314 Total number of prime factors of n*rad(n)+1 counted with multiplicity, where rad = A007947 (squarefree kernel).

1, 1, 2, 2, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 4, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 1, 3, 2, 4, 3, 4, 2, 4, 2, 4, 2, 2, 3, 3, 3, 3, 2, 5, 2, 2, 1, 2, 2, 3, 2, 2, 1, 3, 3, 2, 3, 2, 1, 4, 1, 2, 4, 3, 2, 2, 3, 3, 3, 4, 1, 2, 2, 3, 2, 3, 2, 3, 3, 4, 1, 2, 1, 3, 1, 4, 3, 2, 2, 3, 2, 3

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A007947, A078310, A078313, A078315.

Programs

Haskell

a078314 = a001222 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

a[n_] := PrimeOmega[1 + n * Times @@ FactorInteger[n][[;;, 1]]]; Array[a, 100] (* Amiram Eldar, Sep 08 2024 *)

PARI

a(n)=bigomega(n*vecprod(factor(n)[,1])+1) \\ Charles R Greathouse IV, Jul 09 2013

Formula

a(n) = A001222(A078310(n)).