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A192512 Number of ludic numbers (A003309) not greater than n.

%I A192512 #11 Dec 10 2021 07:24:22
%S A192512 1,2,3,3,4,4,5,5,5,5,6,6,7,7,7,7,8,8,8,8,8,8,9,9,10,10,10,10,11,11,11,
%T A192512 11,11,11,11,11,12,12,12,12,13,13,14,14,14,14,15,15,15,15,15,15,16,16,
%U A192512 16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,19
%N A192512 Number of ludic numbers (A003309) not greater than n.
%H A192512 Reinhard Zumkeller, <a href="/A192512/b192512.txt">Table of n, a(n) for n = 1..10000</a>
%F A192512 a(n) = #{A003309(k): 1<=k<=n} = Sum_{k=1..n} A192490(k).
%t A192512 a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
%t A192512 ludicQ[n_, nmax_] /; 1 <= n <= nmax := MemberQ[a3309[nmax], n];
%t A192512 nmax = 100;
%t A192512 b[n_] := Boole[ludicQ[n, nmax]];
%t A192512 Array[b, nmax] // Accumulate (* _Jean-François Alcover_, Dec 09 2021, after _Ray Chandler_ in A003309 *)
%o A192512 (Haskell)
%o A192512 a192512 n = a192512_list !! (n-1)
%o A192512 a192512_list = scanl1 (+) $ map a192490 [1..]
%Y A192512 Cf. A003309.
%Y A192512 Cf. A192490 (first differences), A000720 (number of primes).
%K A192512 nonn
%O A192512 1,2
%A A192512 _Reinhard Zumkeller_, Jul 05 2011