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 A166062 #59 Feb 16 2025 08:33:11
%S A166062 2,6,30,42,66,2730,510,798,138,870,14322,1919190,13530,1806,282,1590,
%T A166062 354,56786730,64722,4686,140100870,3318,498,61410,4501770,33330,4326,
%U A166062 642,209191710,1671270,4357878,8646,4110,274386,4470,2162622,1794590070,130074
%N A166062 a(n) = denominator(Bernoulli(prime(n) - 1)).
%C A166062 Divisibility through terms of A008578 is a consequence of the Staudt-Clausen theorem.
%C A166062 (Vaguely similar divisibility properties are considered in A165248 and A165943.)
%C A166062 The first 250 entries are all different. Is this true in general?
%C A166062 Would sorting the entries yield the full A090801?
%C A166062 a(n) > 1 is the largest number k such that x*y^p == y*x^p (mod k) for all integers x and y, where p = prime(n). Example: x*y^19 == y*x^19 (mod 798). - _Michel Lagneau_, Apr 19 2012
%C A166062 Comment from _Herbert Kociemba_, May 29 2020: (Start)
%C A166062 For each n there is exactly one member of the sequence whose factorization has prime(n) as its largest prime factor, namely a(n). From this we conclude:
%C A166062 1. All elements of the sequence are different.
%C A166062 2. Not all denominators of Bernoulli numbers appear in this sequence. For example the denominator of B(20), 330=2*3*5*11 never appears because the unique sequence element with largest prime divisor 11=prime(5) is a(5)=2*3*11. (End)
%H A166062 Peter Luschny, <a href="/A166062/b166062.txt">Table of n, a(n) for n = 1..1000</a>
%H A166062 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/vonStaudt-ClausenTheorem.html">von Staudt-Clausen Theorem</a>.
%F A166062 a(n) = A027642(A008578(n) - 1).
%p A166062 seq(denom(bernoulli(ithprime(n)-1)), n=1..38); # _Peter Luschny_, Jul 14 2019
%t A166062 Table[Denominator[BernoulliB[n - 1]], {n, Prime[Range[38]]}] (* _Harvey P. Dale_, Apr 22 2012 *)
%t A166062 Table[GCD @@ Table[(n^k - n), {n, 2, 13}], {k, Prime[Range[100]]}] (* Increase n to 80 and k to 1000 for first thousand terms. - _Herbert Kociemba_, May 05 2020 *)
%t A166062 a[i_] := Times @@ Select[Prime[Range[i]], Mod[Prime[i] - 1, # - 1] == 0&]; Table[a[i], {i, 1, 100}](* _Herbert Kociemba_, May 06 2020 *)
%o A166062 (PARI) a(n)=denominator(bernfrac(prime(n)-1)) \\ _Charles R Greathouse IV_, Apr 30 2012
%Y A166062 Cf. A071772, A110936.
%K A166062 nonn
%O A166062 1,1
%A A166062 _Paul Curtz_, Oct 05 2009
%E A166062 Edited by _Peter Luschny_, Jul 14 2019