A078315 Minimum exponent in prime factorization of n*rad(n)+1, where rad = A007947 (the radical or squarefree kernel).

1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Comments

2 = a(4) = a(45) = a(48) = a(140) = a(529) = a(682) = a(3264) = a(3564) = a(4680) = a(4756) = a(166320) = a(194873) = a(330096) = a(364905) = a(2100332) = a(4160200) with all terms in between equal to 1. Is there an n with a(n) > 2? - Charles R Greathouse IV, May 20 2013

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051904, A078310, A078314, A078316.

Programs

Haskell

a078315 = a051904 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

a[n_] := Min[FactorInteger[1 + n * Times @@ FactorInteger[n][[;;, 1]]][[;;, 2]]]; Array[a, 100] (* Amiram Eldar, Sep 08 2024 *)

PARI

a(n)=my(f=factor(n));f[,2]=apply(n->n+1,f[,2]);vecmin(factor(factorback(f)+1)[,2]) \\ Charles R Greathouse IV, May 20 2013

Formula

a(n) = A051904(A078310(n)).