A124274 - OEIS

%I #12 Dec 10 2024 21:22:20

%S 1,9,15,121

%N Nonprime numbers k that divide A124271(k) = Sum_{i=1..k} (prime(i)^k - 1) / (prime(i) - 1).

%C The next term if it exists is greater than 1000.

%C Note that a(1) = 1, a(2) = 3^2 and a(4) = 11^2 are perfect squares.

%e 9 is a term because 9 divides A124271(9) = 108336139407.

%t s={};Do[If[!PrimeQ[k],If[Divisible[Sum[(Prime[i]^k-1)/(Prime[i]-1),{i,k}],k],AppendTo[s,k]]],{k,10^3}];s (* _James C. McMahon_, Dec 10 2024 *)

%Y Cf. A124271, A124273 (primes p that divide A124271(p)).

%K bref,hard,more,nonn

%O 1,2

%A _Alexander Adamchuk_, Oct 23 2006