A078316 - OEIS

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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

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OFFSET

1,4

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

(Haskell)

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