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%I #12 Apr 06 2020 03:15:18
%S 2,3,5,13,17,31,43,61,83,109,121,125,131,229,239,257,263,269,311,313,
%T 343,361,443,463,503,571,593,599,619,641,647,653,659,701,797,811,853,
%U 953,967,1009,1031,1039,1063,1123,1373,1459,1483,1499,1663,1669,1693
%N Prime powers m such that sigma_4(m^2)/sigma_2(m^2) is prime.
%C Numbers m = p^w such that A001159(m^2)/A001157(m^2) is prime, i.e., m^2 is in A066109.
%C Also m is the square root of a term from A066109 (omitting the term 20). Apart from 20, up to 10000000 A066109 consists of squares of prime powers.
%H Amiram Eldar, <a href="/A066111/b066111.txt">Table of n, a(n) for n = 1..10000</a>
%e m=125: m^2 = 15625 = A066109(13), sigma_4(15625) = 59700165039453751, sigma_2(15625) = 254313151, sigma_4/sigma_2 = 234750601 = A066110(13) is prime. Observe also that sigma_2 is close to sigma_4/sigma_2.
%o (PARI) isok(m) = isprimepower(m) && isprime(sigma(m^2, 4)/sigma(m^2, 2)); \\ _Michel Marcus_, Apr 06 2020
%Y Cf. A001157, A001159, A066109, A066110.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 06 2001
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