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

1,1

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).

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001065, A037020, A252040.

Sequence in context: A060457 A339756 A163369 * A321774 A254267 A028266

Adjacent sequences: A290838 A290839 A290840 * A290842 A290843 A290844

Keyword

nonn

Author

Altug Alkan, Aug 12 2017

Status

approved