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%I #17 Jul 18 2020 04:32:46
%S 16,64,729,2401,4096,15625,28561,65536,83521,262144,279841,531441,
%T 707281,3418801,4826809,9765625,24137569,28398241,38950081,47458321,
%U 244140625,260144641,887503681,1073741824,1387488001,2655237841
%N Squares of composite numbers k such that sigma(k) (sum of divisors of k, A000203) is a prime.
%H Amiram Eldar, <a href="/A065404/b065404.txt">Table of n, a(n) for n = 1..500</a> (terms 1..100 from Harry J. Smith)
%F sigma(a(n)) = A065403(n).
%e 46 cases below 10^12; for M a Mersenne prime, (M+1)/2 is here: M=8191, 4096=(M+1)/2.
%o (PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065404.txt", n++, " ", m^2); if (n==100, return)) ) } \\ _Harry J. Smith_, Oct 18 2009
%Y Cf. A062700, A000203 (sigma), A065403, A065405, A053182, A053183, A028982.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 06 2001
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