A078316 Maximum exponent in the prime factorization of n*rad(n)+1, where rad = A007947 (squarefree kernel).

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

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A007947, A051903, A078310, A078313, A078315.

Programs

Haskell

a078316 = a051903 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

a[n_] := Max[FactorInteger[1 + n * Times @@ FactorInteger[n][[;;, 1]]][[;;, 2]]]; Array[a, 100] (* Amiram Eldar, Sep 07 2024 *)

PARI

a(n) = vecmax(factor(1 + n * vecprod(factorint(n)[, 1]))[, 2]); \\ Amiram Eldar, Sep 07 2024

Formula

a(n) = A051903(A078310(n)).