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
Keywords
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
Programs
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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;}
Comments