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 A332687 #13 Sep 21 2024 08:42:16
%S A332687 1,2,4,6,8,10,13,15,17,19,22,24,27,29,32,35,37,39,42,44,47,50,53,55,
%T A332687 58,60,63,65,68,70,74,76,78,81,84,87,90,92,95,98,101,103,107,109,112,
%U A332687 115,118,120,123,125,128,131,134,136,139,142,145,148,151,153
%N A332687 a(n) = Sum_{k=1..n} ceiling(n/prime(k)).
%F A332687 G.f.: x/(1 - x)^2 + (x/(1 - x)) * Sum_{k>=1} x^prime(k) / (1 - x^prime(k)).
%F A332687 a(n) = n + Sum_{k=1..n-1} omega(k), where omega = A001221.
%F A332687 a(n) = n - omega(n) + Sum_{k=1..n} pi(floor(n/k)), where pi = A000720.
%F A332687 a(n) = n + A013939(n-1) for n >= 2. - _Amiram Eldar_, Sep 21 2024
%t A332687 Table[Sum[Ceiling[n/Prime[k]], {k, 1, n}], {n, 1, 60}]
%t A332687 Table[n + Sum[PrimeNu[k], {k, 1, n - 1}], {n, 1, 60}]
%t A332687 nmax = 60; CoefficientList[Series[x/(1 - x)^2 + (x/(1 - x)) Sum[x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A332687 With[{nmax = 100}, Range[nmax] + Join[{0}, Accumulate[Table[PrimeNu[k], {k, 1, nmax - 1}]]]] (* _Amiram Eldar_, Sep 21 2024 *)
%o A332687 (PARI) a(n) = sum(k=1, n, ceil(n/prime(k))); \\ _Michel Marcus_, Feb 21 2020
%o A332687 (PARI) lista(nmax) = my(s = 1); for(n = 2, nmax, print1(s, ", "); s += omega(n-1) + 1); \\ _Amiram Eldar_, Sep 21 2024
%Y A332687 Cf. A000720, A001221, A006590, A013939, A082767, A083399.
%K A332687 nonn
%O A332687 1,2
%A A332687 _Ilya Gutkovskiy_, Feb 19 2020