%I #29 Oct 07 2017 02:41:35

%S 1,217,57337,600270,621690,669990,685290,693294,693770,699810,725934,

%T 747670,769930,774894,782598,805970,813378,823938,835670,839802,

%U 854930,865490,873334,895594,918435,920414,923410,931634,935715,959565,965174,969034,969206

%N Integers whose sum of divisors is an 8th power.

%H Donovan Johnson, <a href="/A048258/b048258.txt">Table of n, a(n) for n = 1..1000</a>

%H Frits Beukers, Florian Luca and Frans Oort, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.05.373">Power Values of Divisor Sums</a>, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.

%F Sigma(1, a(n)) = x^8, where the initial values of x are 1, 2, 4, 6 (occurs 85 times), ...

%e Divisors(217) = {1,7,31,217}, sum = 256 = 2^8.

%e Divisors(57337) = {1,7,8191,57337}, sum = 65536 = 4^8.

%e Divisors(1676377) = {1,647,2591,1676377}, sum = 1679616 = 6^8.

%t Select[Range[10^6], IntegerQ@ Surd[DivisorSigma[1, #], 8] &] (* _Michael De Vlieger_, Aug 01 2017, after _Harvey P. Dale_ at A048257 *)

%o (PARI) isok(n) = ispower(sigma(n), 8); \\ _Michel Marcus_, Dec 30 2013

%Y Cf. A006532, A020477, A019422, A019423, A019424, A048251-A048257.

%K nonn

%O 1,2

%A _Labos Elemer_