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 A326578 #23 Apr 26 2024 03:14:57
%S A326578 1,2,3,16,5,36,7,64,27,100,11,144,13,196,75,256,17,324,19,400,147,484,
%T A326578 23,576,125,676,243,784,29,900,31,1024,363,1156,1225,1296,37,1444,507,
%U A326578 1600,41,1764,43,1936,135,2116,47,2304,343,2500,867,2704,53,2916,3025
%N A326578 a(n) = n^2*denominator(n*Bernoulli(n-1))/denominator(Bernoulli(n-1)) = n*A326478(n).
%C A326578 Conjecture: If n is Carmichael then a(n) = n.
%C A326578 Are the fixed points of this sequence the numbers satisfying Korselt's criterion?
%H A326578 Peter Luschny, <a href="/A326578/b326578.txt">Table of n, a(n) for n = 1..10000</a>
%F A326578 a(prime(n)) = prime(n).
%F A326578 a(n) = n^2/gcd(n*N(n-1), D(n-1)), with N(k)/D(k) = B(k) the k-th Bernoulli number.
%p A326578 A326578 := n -> n*A326478(n): seq(A326578(n), n=1..55);
%p A326578 db := n -> denom(bernoulli(n)): nb := n -> numer(bernoulli(n)):
%p A326578 a := n -> n^2/igcd(n*nb(n-1), db(n-1)): seq(a(n), n=1..55);
%t A326578 a[n_] := Module[{b = BernoulliB[n - 1]}, n^2 * Denominator[n * b] / Denominator[b]]; Array[a, 60] (* _Amiram Eldar_, Apr 26 2024 *)
%o A326578 (PARI) a(n) = n^2*denominator(n*bernfrac(n-1))/denominator(bernfrac(n-1)); \\ _Michel Marcus_, Jul 17 2019
%Y A326578 Cf. A326478, A326579, A326577, A027641/A027642 (Bernoulli), A002997 (Carmichael), A324050 (Korselt).
%K A326578 nonn
%O A326578 1,2
%A A326578 _Peter Luschny_, Jul 16 2019