This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006590 a(n) = Sum_{k=1..n} ceiling(n/k). (Formerly M2522) 12
 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 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 CROSSREFS Cf. A000005, A006218. Sequence in context: A289037 A060605 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 22:42 EST 2018. Contains 318087 sequences. (Running on oeis4.)