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 A350342 #14 Jan 05 2022 07:18:07
%S A350342 1,2,3,5,7,11,13,17,19,23,29,31,35,37,41,43,47,53,59,61,65,67,71,73,
%T A350342 77,79,83,85,89,97,101,103,107,109,113,115,119,127,131,133,137,139,
%U A350342 143,149,151,157,161,163,167,173,179,181,185,187,191,193,197,199,209
%N A350342 Numbers k such that k^2 is an abelian order.
%C A350342 Such k must be squarefree. Actually, such k must be a cyclic number (A003277).
%C A350342 Number of the form p_1*p_2*...*p_r where the p_i are distinct primes and no (p_j)^2-1 is divisible by any p_i.
%C A350342 The smallest term with exactly n distinct prime factors is given by A350340.
%C A350342 From the term 5 on, no term can be divisible by 2 or 3.
%H A350342 Jianing Song, <a href="/A350342/b350342.txt">Table of n, a(n) for n = 1..10000</a>
%F A350342 A350343(n) = a(n)^2.
%e A350342 For primes p, p is a term since every group of order p^2 is abelian. Such group is isomorphic to either C_{p^2} or C_p X C_p.
%e A350342 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}.
%o A350342 (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 A350342 isA350342(n) = isA051532(n^2)
%Y A350342 Cf. A051532 (abelian orders), A003277 (cyclic numbers), A350343, A350340.
%Y A350342 A350344 is the subsequence of composite numbers.
%K A350342 nonn
%O A350342 1,2
%A A350342 _Jianing Song_, Dec 25 2021