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A238401 Floor(sum(i/(i+1)),i=1..n).

%I A238401 #10 May 18 2023 14:46:32
%S A238401 0,0,1,1,2,3,4,5,6,7,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
%T A238401 24,25,26,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
%U A238401 46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63
%N A238401 Floor(sum(i/(i+1)),i=1..n).
%C A238401 The first numbers which appear twice in the sequence are 0, 1, 7, 26, 77, 220, 608, 1665, 4540, 12356, 33605, 91367, 248383, 675199,... - _Giovanni Resta_, Feb 26 2014
%C A238401 These numbers appear at roughly exp(n - gamma). - _Charles R Greathouse IV_, Feb 26 2014
%H A238401 Giovanni Resta, <a href="/A238401/b238401.txt">Table of n, a(n) for n = 0..1000</a>
%F A238401 a(n) = n - log n + O(1). - _Charles R Greathouse IV_, Feb 26 2014
%e A238401 a(3) = floor(0/1 + 1/2 + 2/3 + 3/4) = floor(1.91666...) = 1.
%t A238401 Floor[Accumulate[Table[i/(i+1),{i,0,70}]]] (* _Harvey P. Dale_, May 18 2023 *)
%o A238401 (JavaScript)
%o A238401 c=0;
%o A238401 for (i=1;i<50;i++) {
%o A238401 c+=i/(i+1);
%o A238401 document.write(Math.floor(c)+", ");
%o A238401 }
%o A238401 (PARI) a(n)=n-ceil(sum(i=2,n,1./i)) \\ _Charles R Greathouse IV_, Feb 26 2014
%Y A238401 Cf. A055980, A001008, A002805.
%K A238401 nonn
%O A238401 0,5
%A A238401 _Jon Perry_, Feb 26 2014
%E A238401 a(50)-a(67) from _Giovanni Resta_, Feb 26 2014