A078315 - OEIS

%I #13 Sep 09 2024 02:40:56

%S 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,

%T 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,

%U 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

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

%C 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

%H Charles R Greathouse IV, <a href="/A078315/b078315.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (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

%o (Haskell)

%o a078315 = a051904 . a078310  -- _Reinhard Zumkeller_, Jul 23 2013

%Y Cf. A051904, A078310, A078314, A078316.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Nov 23 2002