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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A095727 A060457 A163369 * A321774 A254267 A028266 Adjacent sequences:  A290838 A290839 A290840 * A290842 A290843 A290844 KEYWORD nonn AUTHOR Altug Alkan, Aug 12 2017 STATUS approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)