A290841 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.

4, 4, 8, 4, 115, 33, 119, 4, 8, 18, 35, 15, 21, 177, 565, 4, 21, 501, 155, 275, 175, 72, 63, 21, 161, 207, 50, 100, 415, 393, 493, 453, 1250, 33, 75, 15, 85, 777, 655, 351, 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

Offset: 1

Author

Altug Alkan, Aug 12 2017

Keywords

• nonn

Comments

Corresponding primes are 3, 5, 73, 17, 6439469, 1772291, 411162217, 257, ...

a(n) = 4 if and only if 2^n + 1 is a Fermat prime (A019434).

Examples

			a(5) = 115 because 1^5 + 5^5 + 23^5 = 6439469 is prime and 115 is the smallest number with this property.
		

Links

• Iain Fox, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001065, A037020, A252040.

Programs

Mathematica

Table[SelectFirst[Range[10^4], PrimeQ[DivisorSigma[n, #] - #^n] &], {n, 69}] (* Michael De Vlieger, Aug 14 2017 *)

PARI

a(n) = {my(k=1); while(!isprime(sigma(k,n)-k^n), k++); k;}