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 A094820 Partial sums of A038548. 13
 1, 2, 3, 5, 6, 8, 9, 11, 13, 15, 16, 19, 20, 22, 24, 27, 28, 31, 32, 35, 37, 39, 40, 44, 46, 48, 50, 53, 54, 58, 59, 62, 64, 66, 68, 73, 74, 76, 78, 82, 83, 87, 88, 91, 94, 96, 97, 102, 104, 107, 109, 112, 113, 117, 119, 123, 125, 127, 128, 134, 135, 137, 140, 144, 146, 150 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = number of pairs (c,d) of integers such that 0 < c <= d and c*d <= n. - Clark Kimberling, Jun 18 2011 Equivalently, the number of representations of n in the form x + y*z, where x, y, and z are positive integers and y <= z. - John W. Layman, Feb 21 2012 LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 Vaclav Kotesovec, Graph - the asymptotic ratio (100000 terms) FORMULA G.f.: (1/(1 - x))*Sum_{k>=1} x^(k^2)/(1 - x^k). - Ilya Gutkovskiy, Apr 13 2017 a(n) ~ (log(n) + 2*gamma - 1)*n/2 + sqrt(n)/2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Aug 19 2019 MAPLE ListTools:-PartialSums([seq(ceil(numtheory:-tau(n)/2), n=1..100)]); # Robert Israel, Feb 24 2016 MATHEMATICA f[n_, k_] := Floor[n/k] - Floor[(n - 1)/k] g[n_, k_] := If[k^2 <= n, f[n, k], 0] Table[Sum[f[n, k], {k, 1, n}], {n, 1, 100}] (* A000005 *) t = Table[Sum[g[n, k], {k, 1, n}], {n, 1, 100}] (* A038548 *) a[n_] := Sum[t[[i]], {i, 1, n}] Table[a[n], {n, 1, 100}]  (* A094820 *) (* from Clark Kimberling, Jun 18 2011 *) Table[Sum[Boole[d <= Sqrt[n]], {d, Divisors[n]}], {n, 1, 66}] // Accumulate (* Jean-François Alcover, Dec 13 2012 *) PROG (Ruby)   def a(n)     (1..Math.sqrt(n)).inject(0) { |accum, i| accum + 1 + (n/i).to_i - i }   end # Peter Kagey, Feb 24 2016 (PARI) a(n) = sum(k=1, n, ceil(numdiv(k)/2)); \\ Michel Marcus, Feb 24 2016 CROSSREFS Cf. A091626, A038548. Sequence in context: A050172 A191877 A277124 * A309793 A093689 A097702 Adjacent sequences:  A094817 A094818 A094819 * A094821 A094822 A094823 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jun 12 2004 STATUS approved

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)