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 A350345 #14 Jan 05 2022 05:32:23
%S A350345 1225,4225,5929,7225,13225,14161,17689,20449,25921,34225,34969,43681,
%T A350345 46225,47089,48841,55225,61009,67081,70225,89401,101761,104329,108241,
%U A350345 112225,116281,133225,137641,142129,152881,162409,165649,170569,172225,182329,190969
%N A350345 Squares of composite numbers k that are abelian orders.
%C A350345 Square numbers k that are abelian orders with at least 4 groups.
%C A350345 Number of the form (p_1*p_2*...*p_r)^2 where r > 1, the p_i are distinct primes and no (p_j)^2-1 is divisible by any p_i.
%C A350345 The smallest square number k that is an abelian order with at least 8 groups is A350341(3) = 354025.
%C A350345 No term can be divisible by 2 or 3.
%H A350345 Jianing Song, <a href="/A350345/b350345.txt">Table of n, a(n) for n = 1..10000</a>
%F A350345 a(n) = A350344(n)^2.
%e A350345 For primes p, q, if p^2 !== 1 (mod q), q^2 !== 1 (mod p), then p^2*q^2 is a term since every group of that order is abelian. Such group is isomorphic to C_{p^2*q^2}, C_p X C_{p*q^2}, C_q X C_{p^2*q} or C_{p*q} X C_{p*q}.
%o A350345 (PARI) isA051532(n) = my(f=factor(n), v=vector(#f[, 1])); for(i=1, #v, if(f[i, 2]>2, return(0), v[i]=f[i, 1]^f[i, 2])); for(i=1, #v, for(j=i+1, #v, if(v[i]%f[j, 1]==1 || v[j]%f[i, 1]==1, return(0)))); 1 \\ _Charles R Greathouse IV_'s program for A051532
%o A350345 isA350345(n) = issquare(n) && (n>1) && !isprime(sqrtint(n)) && isA051532(n^2)
%Y A350345 Cf. A051532 (abelian orders), A050384, A350341.
%Y A350345 Equals A350343 \ ({1} U A001248).
%Y A350345 A350323 is a subsequence.
%K A350345 nonn
%O A350345 1,1
%A A350345 _Jianing Song_, Dec 25 2021