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 A006590 a(n) = Sum_{k=1..n} ceiling(n/k). (Formerly M2522) 25
 1, 3, 6, 9, 13, 16, 21, 24, 29, 33, 38, 41, 48, 51, 56, 61, 67, 70, 77, 80, 87, 92, 97, 100, 109, 113, 118, 123, 130, 133, 142, 145, 152, 157, 162, 167, 177, 180, 185, 190, 199, 202, 211, 214, 221, 228, 233, 236, 247, 251, 258, 263, 270, 273, 282, 287, 296, 301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446. - Jeremy Gardiner, Mar 16 2003 Given the fact that ceiling(x) <= x+1, we can, using well known results for the harmonic series, easily derive that n*log(n) <= a(n) <= n*(1+log(n)) + n = n(log(n)+2). - Stefan Steinerberger, Apr 08 2006 REFERENCES Marc LeBrun, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 M. Le Brun, Email to N. J. A. Sloane, Jul 1991 FORMULA a(n) = n+Sum_{k=1..n-1} tau(k). - Vladeta Jovovic, Oct 17 2002 a(n) = 1 + a(n-1) + tau(n-1), a(n) = A006218(n-1) + n. - T. D. Noe, Jan 05 2007 a(n) = a(n-1) + A000005(n) + 1 for n >= 2. a(n) = A161886(n) - A000005(n) + 1 = A161886(n-1) + 2 = A006218(n) + A049820(n) for n >= 1. - Jaroslav Krizek, Nov 14 2009 MAPLE seq(add(ceil(n/j), j = 1..n), n = 1..60); # G. C. Greubel, Nov 07 2019 MATHEMATICA Table[Sum[Ceiling[n/i], {i, 1, n}], {n, 1, 60}] (* Stefan Steinerberger, Apr 08 2006 *) nxt[{n_, a_}]:={n+1, a+DivisorSigma[0, n]+1}; Transpose[NestList[nxt, {1, 1}, 60]][[2]] (* Harvey P. Dale, Aug 23 2013 *) PROG (Haskell) a006590 n = sum \$ map f [1..n] where    f x = y + 1 - 0 ^ r where (y, r) = divMod n x -- Reinhard Zumkeller, Feb 18 2013 (PARI) first(n)=my(v=vector(n, i, i), s); for(i=1, n-1, v[i+1]+=s+=numdiv(i)); v \\ Charles R Greathouse IV, Feb 07 2017 (MAGMA) [&+[Ceiling(n/j): j in [1..n]] : n in [1..60]]; // G. C. Greubel, Nov 07 2019 (Sage) [sum(ceil(n/j) for j in (1..n)) for n in (1..60)] # G. C. Greubel, Nov 07 2019 CROSSREFS Cf. A000005, A006218. Sequence in context: A060605 A325228 A278449 * A061781 A123753 A124288 Adjacent sequences:  A006587 A006588 A006589 * A006591 A006592 A006593 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from Stefan Steinerberger, Apr 08 2006 STATUS approved

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Last modified September 18 23:30 EDT 2020. Contains 337175 sequences. (Running on oeis4.)