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 A350344 #14 Jan 11 2022 22:14:30
%S A350344 35,65,77,85,115,119,133,143,161,185,187,209,215,217,221,235,247,259,
%T A350344 265,299,319,323,329,335,341,365,371,377,391,403,407,413,415,427,437,
%U A350344 451,469,481,485,493,511,515,517,527,533,535,551,553,559,565,583,589,595
%N A350344 Composite k such that k^2 is an abelian order.
%C A350344 Numbers k such that k^2 is an abelian order with at least 4 groups.
%C A350344 Number of the form p_1*p_2*...*p_r where r > 1, the p_i are distinct primes and no (p_j)^2-1 is divisible by any p_i.
%C A350344 The smallest number k such that k^2 is an abelian order with at least 8 groups is A350340(3) = 595.
%C A350344 No term can be divisible by 2 or 3.
%H A350344 Jianing Song, <a href="/A350344/b350344.txt">Table of n, a(n) for n = 1..10000</a>
%F A350344 A350345(n) = a(n)^2.
%e A350344 For primes p, q, if p^2 !== 1 (mod q), q^2 !== 1 (mod p), then p*q 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}.
%e A350344 95 is not a term since 95^2 = 5^2 * 19^2 is not an abelian order. Note that 95 itself is a cyclic number.
%o A350344 (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 A350344 isA350344(n) = (n>1) && !isprime(n) && isA051532(n^2)
%Y A350344 Cf. A051532 (abelian orders), A050384, A350340.
%Y A350344 Equals A350342 \ ({1} U A000040).
%K A350344 nonn
%O A350344 1,1
%A A350344 _Jianing Song_, Dec 25 2021