%I #15 Jul 16 2021 17:12:30
%S 213556659624,359544809085,1329797339640,1548635130140,1746049287480,
%T 1810001934510,1867318744632,1875874796664,1909975290390,
%U 2040256862622,2516452216712,3407803953785,6329875033944,7792308679512,7840198408728,7877108796312,8098434291288,8241610823832
%N Numbers k such that sigma(k) is the fifth power of the sum of the prime divisors of k.
%C The smallest k for which sigma(k) = sopf(k)^6 is 45770980141656. Other such values are 5245619666623908 and 5582294774581035.
%H Robert Gerbicz, <a href="/A221263/b221263.txt">Table of n, a(n) for n = 1..10000</a>
%e 213556659624 = 2^3*3^3*7^3*11*31*79*107 and sigma(213556659624) = (2+3+7+11+31+79+107)^5.
%Y Cf. A000203, A008472.
%Y Cf. A187771 (sigma(k)=sopf(k)^3), A221262 (sigma(k)=sopf(k)^4).
%K nonn
%O 1,1
%A _Giovanni Resta_, Jan 07 2013