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%I #24 Jul 23 2016 11:49:57
%S 2,4,64,289,729,15625,7091569,7778521,11607649,15912121,43546801,
%T 56957209,138980521,143688169,171845881,210801361,211673401,253541929,
%U 256224049,275792449,308810329,329386201,357172201,408807961,499477801,531625249,769341169,1073741824,1260747049
%N Numbers n such that sigma(n) and sigma(n^2) are primes.
%C Intersection of A023194 and A055638.
%C Sigma(n) = A000203(n) = sum of divisors of n.
%C Terms a(2)...a(29) are squares of 2, 8, 17, 27, 125, 2663, 2789, 3407, 3989, 6599, 7547, 11789, 11987, 13109, 14519, 14549, 15923, 16007, 16607, 17573, 18149, 18899, 20219, 22349, 23057, 27737, 32768, 35507.
%H Donovan Johnson and Chai Wah Wu, <a href="/A232444/b232444.txt">Table of n, a(n) for n = 1..10385</a> [Terms from 1 to 500 from Donovan Johnson]
%e 4 is in the sequence because both sigma(4)=7 and sigma(4^2)=31 are primes.
%o (PARI) isok(n) = isprime(sigma(n)) && isprime(sigma(n^2)); \\ _Michel Marcus_, Nov 26 2013
%o (Python)
%o from sympy import isprime, divisor_sigma
%o A232444_list = [2]+[n for n in (d**2 for d in range(1,10**4)) if isprime(divisor_sigma(n)) and isprime(divisor_sigma(n**2))] # _Chai Wah Wu_, Jul 23 2016
%Y Cf. A000203, A023194, A055638.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Nov 24 2013
%E a(6)-a(12) from _Michel Marcus_, Nov 26 2013
%E a(13)-a(29) from _Alex Ratushnyak_, Nov 26 2013
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