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

1,3

Comments

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

Links

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

Mathematica

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

Prog

(PARI) a(n)=omega(n*vecprod(factor(n)[, 1])+1) \\ Charles R Greathouse IV, Jul 09 2013
(Haskell)
a078313 = a001221 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Crossrefs

Cf. A078314, A078315.

Sequence in context: A226898 A338653 A033111 * A354601 A025827 A025826

Adjacent sequences: A078310 A078311 A078312 * A078314 A078315 A078316

Keyword

nonn

Author

Reinhard Zumkeller, Nov 23 2002

Status

approved