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 A117897 #12 Oct 09 2021 16:00:40
%S A117897 1,4,129,16936,2357964627,1794518358664,2862424846028174457,
%T A117897 5483249282630830360396,39471589603944768518079950019,
%U A117897 3053134546009996125349281528007992109928
%N A117897 Number of labeled trees on prime numbers of nodes through n-th prime.
%C A117897 A000178 = Sum_{k=1..n} k^(k-1). A001923 = Sum_{k=1..n} k^k. A061789 = Sum_{k=1..n} prime(k)^prime(k), prime(k) = k-th prime.
%C A117897 First differences a(n+1) - a(n) for n=1,...,9 are A076931(j) at j=3, 5, 7, 11, 13, 17, 19, 23 and 29. - _R. J. Mathar_, May 01 2007
%H A117897 G. C. Greubel, <a href="/A117897/b117897.txt">Table of n, a(n) for n = 1..75</a>
%F A117897 a(n) = Sum_{k=1..n} prime(k)^(prime(k)-2).
%F A117897 a(n) = Sum_{k=1..n} A000272(A000040(k)).
%e A117897 a(1) = number of labeled trees on prime(1) numbers of nodes = number of labeled trees on 2 nodes = A000272(2) = 2^0 = 1.
%e A117897 a(2) = number of labeled trees on prime(1) or prime(2) numbers of nodes = number of labeled trees on 2 or 3 nodes = A000272(2)+A000272(3) = 2^0 + 3^1 = 4.
%e A117897 a(3) = number of labeled trees on prime(1) or prime(2) or prime(3) numbers of nodes = number of labeled trees on 2 or 3 or 5 nodes = A000272(2)+A000272(3)+A000272(5) = 2^0 + 3^1 + 5^3 = 129.
%t A117897 Table[Sum[Prime[k]^(Prime[k] -2), {k,n}], {n,20}] (* _G. C. Greubel_, Sep 27 2021 *)
%o A117897 (Sage) [sum( nth_prime(k)^(nth_prime(k) -2) for k in (1..n)) for n in (1..20)] # _G. C. Greubel_, Sep 27 2021
%Y A117897 Cf. A000040, A000178, A000272, A001923, A061789.
%K A117897 easy,nonn
%O A117897 1,2
%A A117897 _Jonathan Vos Post_, May 03 2006