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 A350323 #16 Jan 05 2022 13:50:59
%S A350323 1225,4225,5929,7225,13225,14161,15925,17689,20449,20825,23275,25921,
%T A350323 28175,34225,34969,43681,45325,46225,47089,48841,50575,55225,57575,
%U A350323 61009,64925,67081,70225,70805,71825,72275,77077,80275,82075,89401,89425,92575,93925,96775,97175
%N A350323 Abelian orders m for which there exist at least 4 groups of order m.
%C A350323 Abelian orders of the form (p_1)^2 * (p_2)^2 * ... * (p_r)^2 * q_1 * q_2 * ... * q_s, r >= 2, where p, q_1, q_2, ..., q_s are distinct primes such that p^2 !== 1 (mod q_j), q_i !== 1 (mod p_j), q_i !== 1 (mod q_j) for i != j. Note that there are 2^r groups of such order.
%C A350323 No term can be divisible by 2 or 3.
%H A350323 Jianing Song, <a href="/A350323/b350323.txt">Table of n, a(n) for n = 1..10000</a>
%e A350323 For primes p, q, if p^2 !== 1 (mod q) and q^2 !== 1 (mod p), then p^2*q^2 is a term since the 4 groups of that order are C_{p^2*q^2}, C_p X C_{p*q^2}, C_q X C_{p^2*q}, C_{p*q} X C_{p*q}.
%o A350323 (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 A350323 isA350323(n) = isA051532(n) && (bigomega(n)-omega(n)>1)
%Y A350323 Equals A350152 \ A350322 = A051532 \ (A005117 U A060687).
%K A350323 nonn
%O A350323 1,1
%A A350323 _Jianing Song_, Dec 25 2021