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 A378721 #11 Dec 06 2024 11:30:15
%S A378721 1,1,30,30,165,15015,36465,62985,7436429,11849255,73465381,
%T A378721 33426748355,50708377254535,436092044389001,1863302371480277,
%U A378721 1086305282573001491,64092011671807087969,3909612711980232366109,8449808119441147371913,18598027670889965365580513,3543193335582015099413
%N A378721 a(n) is the denominator of the asymptotic density of numbers whose third smallest prime divisor is prime(n).
%C A378721 See A378720 for more details.
%H A378721 Amiram Eldar, <a href="/A378721/b378721.txt">Table of n, a(n) for n = 1..365</a>
%t A378721 a[n_] := Block[{p, q = Prime@ Range@ n}, p = Fold[Times, 1, q]; q = Most@ q; Plus @@ Times @@@ Subsets[q -1, {n -3}]/p]; a[1] = 0; Denominator@ Array[a, 21]
%o A378721 (PARI) a(n) = {my(v = primes(n), q = vecextract(apply(x -> x-1, v),"^-1"), p = vecprod(v), prd = vecprod(q)/p, sm = 0, sb); forsubset([#q, 2], s, sb = vecextract(q, s); sm += 1/vecprod(sb)); denominator(prd * sm);}
%Y A378721 Cf. A000040, A038110, A038111, A342479, A342480, A378720 (numerators).
%K A378721 nonn,easy,frac
%O A378721 1,3
%A A378721 _Robert G. Wilson v_ and _Amiram Eldar_, Dec 05 2024