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%I #20 Nov 15 2017 04:29:49
%S 4,4,8,4,115,33,119,4,8,18,35,15,21,177,565,4,21,501,155,275,175,72,
%T 63,21,161,207,50,100,415,393,493,453,1250,33,75,15,85,777,655,351,
%U 649,833,327,219,1727,123,57,15,21,357,183,1113,50,87,57,135,831,291,341,196,175,249,2107,783,57,927,800,39,209
%N a(n) is the least number k such that the sum of the n-th powers of the proper divisors of k is a prime number.
%C Corresponding primes are 3, 5, 73, 17, 6439469, 1772291, 411162217, 257, ...
%C a(n) = 4 if and only if 2^n + 1 is a Fermat prime (A019434).
%H Iain Fox, <a href="/A290841/b290841.txt">Table of n, a(n) for n = 1..1000</a>
%e a(5) = 115 because 1^5 + 5^5 + 23^5 = 6439469 is prime and 115 is the smallest number with this property.
%t Table[SelectFirst[Range[10^4], PrimeQ[DivisorSigma[n, #] - #^n] &], {n, 69}] (* _Michael De Vlieger_, Aug 14 2017 *)
%o (PARI) a(n) = {my(k=1); while(!isprime(sigma(k,n)-k^n), k++); k;}
%Y Cf. A001065, A037020, A252040.
%K nonn
%O 1,1
%A _Altug Alkan_, Aug 12 2017
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