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 A023538 #14 Jul 11 2020 02:29:42
%S A023538 1,4,10,21,39,68,110,169,247,348,478,639,837,1076,1358,1687,2069,2510,
%T A023538 3012,3581,4221,4934,5726,6601,7565,8626,9788,11053,12425,13906,15500,
%U A023538 17221,19073,21062,23190,25467,27895,30480,33228,36143,39231,42498,45946,49585
%N A023538 Convolution of natural numbers with (1, p(1), p(2), ... ), where p(k) is the k-th prime.
%H A023538 F. Javier de Vega, <a href="https://arxiv.org/abs/2003.13378">An extension of Furstenberg's theorem of the infinitude of primes</a>, arXiv:2003.13378 [math.NT], 2020.
%F A023538 a(n) = Sum_{k<=n} [(A158611(k+1)) * (A000027(n-k+1))] = Sum_{k<=n} [(A008578(k)) * (A000027(n-k+1))]. [_Jaroslav Krizek_, Aug 05 2009; Correction for change of offset in A158611 and A008578 in Aug 2009 _Jaroslav Krizek_, Jan 27 2010]
%t A023538 Nest[Accumulate,Join[{1},Select[Range@200,PrimeQ]],2] (* _Vladimir Joseph Stephan Orlovsky_, Jan 25 2012 *)
%Y A023538 Cf. A007504, A014148, A014150, A014284, A023538, A178138.
%K A023538 nonn
%O A023538 1,2
%A A023538 _Clark Kimberling_