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 A059851 a(n) = n - floor(n/2) + floor(n/3) - floor(n/4) + ... (this is a finite sum). 14
 0, 1, 1, 3, 2, 4, 4, 6, 4, 7, 7, 9, 7, 9, 9, 13, 10, 12, 12, 14, 12, 16, 16, 18, 14, 17, 17, 21, 19, 21, 21, 23, 19, 23, 23, 27, 24, 26, 26, 30, 26, 28, 28, 30, 28, 34, 34, 36, 30, 33, 33, 37, 35, 37, 37, 41, 37, 41, 41, 43, 39, 41, 41, 47, 42, 46, 46, 48, 46, 50, 50, 52, 46, 48, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS As n goes to infinity we have the asymptotic formula: a(n) ~ n * log(2). LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A006218(n)-2*A006218(floor(n/2)). G.f.: 1/(1-x)*Sum_{n>=1} x^n/(1+x^n). Partial sums of A048272. - Vladeta Jovovic, Oct 15 2002 a(n) = Sum_{n/2 < k < =n} d(k) - Sum_{1 < =k <= n/2} d(k), where d(k) = A000005(k). Also, a(n) = number of terms among {floor(n/k)}, 1<=k<=n, that are odd. - Leroy Quet, Jan 19 2006 From Ridouane Oudra, Aug 15 2019: (Start) a(n) = Sum_{k=1..n} (floor(n/k) mod 2) a(n) = (n/2) + (1/2)*A271860(n) a(n) =  Sum_{k=1..n} round(n/(2*k)) - floor(n/(2*k)), where round(1/2)=1. (End) EXAMPLE a(5) = 4 because floor(5) - floor(5/2) + floor(5/3) - floor(5/4) + floor(5/5) - floor(5/6) + ... = 5 - 2 + 1 - 1 + 1 - 0 + 0 - 0 + ... = 4. MAPLE for n from 0 to 200 do printf(`%d, `, sum((-1)^(i+1)*floor(n/i), i=1..n)) od: { for (n=0, 10000, s=1; d=2; a=n; while ((f=floor(n/d)) > 0, a-=s*f; s=-s; d++); write("b059851.txt", n, " ", a); ) } # Harry J. Smith, Jun 29 2009 MATHEMATICA f[list_, i_] := list[[i]]; nn = 200; a = Table[1, {n, 1, nn}]; b = Table[If[OddQ[n], 1, -1], {n, 1, nn}]; Table[DirichletConvolve[f[a, n], f[b, n], n, m], {m, 1, nn}] // Accumulate (* Geoffrey Critzer, Mar 29 2015 *) Table[Sum[Floor[n/k] - 2*Floor[n/(2*k)], {k, 1, n}], {n, 0, 100}] (* Vaclav Kotesovec, Dec 23 2020 *) PROG (PARI) { for (n=0, 10000, s=1; d=2; a=n; while ((f=floor(n/d)) > 0, a-=s*f; s=-s; d++); write("b059851.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 29 2009 CROSSREFS Cf. A075997. Partial sums of A048272. Sequence in context: A069745 A112199 A145815 * A327637 A047993 A033177 Adjacent sequences:  A059848 A059849 A059850 * A059852 A059853 A059854 KEYWORD nonn,easy AUTHOR Avi Peretz (njk(AT)netvision.net.il), Feb 27 2001 EXTENSIONS More terms from James A. Sellers and Larry Reeves (larryr(AT)acm.org), Feb 27 2001 STATUS approved

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Last modified May 6 07:01 EDT 2021. Contains 343580 sequences. (Running on oeis4.)