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 A030009 #24 Jul 08 2025 19:26:44
%S A030009 1,2,6,15,37,85,192,414,879,1816,3694,7362,14480,28037,53644,101379,
%T A030009 189587,350874,643431,1169388,2108045,3770430,6694894,11804968,
%U A030009 20679720,35999794,62298755,107198541,183462856,312357002,529173060,892216829,1497454396,2502190992
%N A030009 Euler transform of primes.
%H A030009 Alois P. Heinz, <a href="/A030009/b030009.txt">Table of n, a(n) for n = 0..1000</a>
%H A030009 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A030009 G.f.: Product_{n>=1} (1-x^n)^(-prime(n)).
%p A030009 with(numtheory):
%p A030009 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A030009 d*ithprime(d), d=divisors(j))*a(n-j), j=1..n)/n)
%p A030009 end:
%p A030009 seq(a(n), n=0..40); # _Alois P. Heinz_, Sep 06 2008
%t A030009 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*Prime[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Apr 16 2014, after _Alois P. Heinz_ *)
%o A030009 (PARI) a(n)=if(n<0,0,polcoeff(prod(i=1,n,(1-x^i)^-prime(i),1+x*O(x^n)),n))
%o A030009 (SageMath) # uses[EulerTransform from A166861]
%o A030009 b = EulerTransform(lambda n: nth_prime(n))
%o A030009 print([b(n) for n in range(37)]) # _Peter Luschny_, Nov 11 2020
%Y A030009 Cf. A007441.
%K A030009 nonn
%O A030009 0,2
%A A030009 _N. J. A. Sloane_