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 A378053 #10 Nov 15 2024 11:17:16
%S A378053 1,1,2,3,4,2,2,3,16,36,2,30,4,6,16,45,4,80,2,108,16,6,2,210,24,12,32,
%T A378053 18,4,1008,2,45,64,12,48,8400,4,18,16,2268,4,240,2,90,512,18,2,3150,
%U A378053 32,216,64,540,4,160,144,2430,32,12,2,166320,4,6,1280,405,48,1344
%N A378053 a(n) = gcd(Product_{d|n} (d + 1), Product_{d|n, d>1} (d - 1)) = gcd(A020696(n), A377484(n)).
%H A378053 Amiram Eldar, <a href="/A378053/b378053.txt">Table of n, a(n) for n = 1..10000</a>
%F A378053 a(n) = 2 if and only if n = 6 or n is a prime of the form 4*k+3 (A002145).
%F A378053 a(n) = 4 if and only if n is a prime of the form 4*k+1 (A002144).
%F A378053 a(n) == 1 (mod 2) if and only if n is a power of 2 (A000079).
%t A378053 a[n_] := GCD[Times @@ ((d = Divisors[n]) + 1), Times @@ (Rest@ d - 1)]; Array[a, 70]
%o A378053 (PARI) a(n) = if(n == 1, 1, my(d = divisors(n)); gcd(prod(k=1, #d, d[k]+1), prod(k=2, #d, d[k]-1)));
%Y A378053 Cf. A000079, A002144, A002145, A020696, A377484, A378056.
%K A378053 nonn
%O A378053 1,3
%A A378053 _Amiram Eldar_, Nov 15 2024