cp's OEIS Frontend

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

%I A078315 #13 Sep 09 2024 02:40:56
%S A078315 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 A078315 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 A078315 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 A078315 Minimum exponent in prime factorization of n*rad(n)+1, where rad = A007947 (the radical or squarefree kernel).
%C A078315 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 A078315 Charles R Greathouse IV, <a href="/A078315/b078315.txt">Table of n, a(n) for n = 1..10000</a>
%F A078315 a(n) = A051904(A078310(n)).
%t A078315 a[n_] := Min[FactorInteger[1 + n * Times @@ FactorInteger[n][[;;, 1]]][[;;, 2]]]; Array[a, 100] (* _Amiram Eldar_, Sep 08 2024 *)
%o A078315 (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 A078315 (Haskell)
%o A078315 a078315 = a051904 . a078310  -- _Reinhard Zumkeller_, Jul 23 2013
%Y A078315 Cf. A051904, A078310, A078314, A078316.
%K A078315 nonn
%O A078315 1,4
%A A078315 _Reinhard Zumkeller_, Nov 23 2002