A231333 - OEIS

%I #25 Aug 07 2018 12:16:29

%S 1,0,0,1,0,2,0,3,2,4,0,15,0,6,4,7,0,40,0,9,6,10,0,77,4,12,8,39,0,630,

%T 0,15,10,16,12,187,0,18,12,133,0,260,0,21,56,22,0,345,6,72,16,75,0,

%U 442,20,189,18,28,0,6061,0,30,40,31,12,3360,0,33,22,3978

%N a(n) = lcm_{p is a prime divisor of n} (n/p - 1).

%C n is prime if and only if a(n) = 0.

%C n is a Giuga number if and only if a(n) > 0 and n divides a(n).

%H Andrew Howroyd, <a href="/A231333/b231333.txt">Table of n, a(n) for n = 1..1000</a>

%F a(6) = 2 because 6/2 - 1 = 2 and 6/3 - 1 = 1, and the least common multiple of 2 and 1 is 2.

%F a(7) = 0 because 7/7 - 1 = 0.

%F a(8) = 3 because 8/2 - 1 = 3.

%t lcm[lis_] := {aux = 1; Do[aux = LCM[aux, lis[[i]]], {i, 1, Length[lis]}]; aux}[[1]]; fa = FactorInteger; j[n_] := lcm@Table[n/fa[n][[i, 1]] - 1, {i, 1, Length[fa[n]]}] ; Array[j, 100]

%o (PARI) a(n)=my(f=factor(n)[,1]); lcm(vector(#f,i,n/f[i]-1)) \\ _Charles R Greathouse IV_, Nov 13 2013

%Y Cf. A007850.

%K nonn

%O 1,6

%A _José María Grau Ribas_, Nov 07 2013