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 A352587 #39 Apr 24 2023 05:34:56 %S A352587 2,4,6,10,16,18,20,28,60,84,228,240,280,366,420,468,484,604,684,942, %T A352587 990,1152,1170,1196,1440,2064,5292,5954,8968,9176,13242,13680,14160, %U A352587 15190,24524,28764,29422,30558,30646,34804,35190,38164,44642,56772,62790,93024 %N A352587 Even numbers 2m such that A352612(2m) = A103131(2m). %C A352587 Any counterexample to the Goldbach conjecture must have this form. %C A352587 Conjecture: For all a(n) > 18, a(n) is never equal to 2*q^x where q is prime and x is an integer x > 0. In other words, the product of its totatives is never congruent to -1 (mod 2m). %H A352587 Craig J. Beisel, <a href="/A352587/b352587.txt">Table of n, a(n) for n = 1..56</a> %e A352587 For a(1) we have A352612(228) == -(59)(85) (mod 228) == 1 (mod 228) == A103131(228). Therefore A352612(228) == A103131(228) and 228 belongs to the sequence. %o A352587 (PARI) for(n=1,150000, prod_t=1; prod_p=1; prod_r=1; for(k=3, 2*n-3, if(gcd(k,2*n)==1, prod_t=prod_t*k; ); if(gcd(k,2*n)==1 && isprime(k), prod_p=prod_p*k*(2*n-k); ); if(gcd(k,2*n)==1 && !isprime(k) && !isprime(2*n-k), prod_r=prod_r*k; ); ); if(-prod_t%(2*n)==(-prod_p*prod_r)%(2*n), print1(2*n,","); ); ); %Y A352587 Cf. A103131, A141098, A352612. %K A352587 nonn %O A352587 1,1 %A A352587 _Craig J. Beisel_, Mar 21 2022