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 A065772 #14 Apr 13 2024 05:15:27
%S A065772 9,25,32,121,243,343,361,961,1331,1369,1681,2048,2209,2809,3481,3721,
%T A065772 4489,5041,6561,6859,7921,9409,10201,10609,11449,11881,12167,12769,
%U A065772 16384,16807,17161,18769,19321,19683,22201,22801,24389,24649,26569
%N A065772 Nontrivial prime powers k from A025475 such that tau(k^2) is prime but sigma(k^2) is a composite number.
%C A065772 Numbers k = A025475(m) such that A000005(k^2) is prime but A000203(k^2) is composite number.
%H A065772 Amiram Eldar, <a href="/A065772/b065772.txt">Table of n, a(n) for n = 1..10000</a>
%e A065772 For k = 32: k^2 = 1024, tau(1024) = 11, sigma(1024) = 2047 = 23*89.
%e A065772 For k = 243, k^2 = 59049, tau(59049) = 11, sigma(59049) = 88573 = 23*3851.
%e A065772 Up to 10000000, 453 terms were found.
%t A065772 Do[ s=DivisorSigma[ 0, n^2 ]; y=DivisorSigma[ 1, n^2 ]; If[ Equal[ Length[ FactorInteger[ n ] ], 1 ]&&!PrimeQ[ n ] &&PrimeQ[ s ]&&!PrimeQ[ y ], Print[ n ] ], {n, 1, 10000000} ]
%Y A065772 Cf. A000005 (tau), A000203 (sigma), A065403, A065404, A065405, A028982, A025475.
%K A065772 nonn
%O A065772 1,1
%A A065772 _Labos Elemer_, Nov 19 2001