This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065405 #21 Dec 18 2024 22:36:17
%S A065405 4,8,27,49,64,125,169,256,289,512,529,729,841,1849,2197,3125,4913,
%T A065405 5329,6241,6889,15625,16129,29791,32768,37249,51529,57121,69169,76729,
%U A065405 113569,117649,128881,139129,157609,192721,208849,226981,229441,253009
%N A065405 Composite numbers k such that the sum of the divisors of k^2 is a prime.
%C A065405 All these composite numbers k should be prime powers because if k=a*b with gcd(a,b)=1, then sigma(aabb) = sigma(aa)*sigma(bb) cannot be a prime; 46 of the 236 prime powers below 1000000 are here.
%H A065405 Amiram Eldar, <a href="/A065405/b065405.txt">Table of n, a(n) for n = 1..500</a> (terms 1..70 from Harry J. Smith)
%F A065405 sigma(a(n)^2) = sigma(A065404(n)) = A065403(n) is prime.
%t A065405 Select[ Range[3 10^5], ! PrimeQ[ # ] && PrimeQ[ DivisorSigma[1, #^2]] & ]
%o A065405 (PARI) isok(k) = { !isprime(k) && isprime(sigma(k^2)) } \\ _Harry J. Smith_, Oct 18 2009
%Y A065405 Cf. A062700, A000203, A065403, A065404, A053182, A053183, A028982.
%K A065405 nonn
%O A065405 1,1
%A A065405 _Labos Elemer_, Nov 06 2001