A078313 Number of distinct prime factors of n*rad(n)+1, where rad=A007947 (squarefree kernel).

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

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Comments

a(n)=A001221(A078310(n)).

Links

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

Crossrefs

Cf. A078314, A078315.

Programs

Haskell

a078313 = a001221 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

A078313[n_] := PrimeNu[n*Times @@ FactorInteger[n][[All, 1]] + 1]; Array[A078313, 50] (* G. C. Greubel, Apr 25 2017 *)

PARI

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