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 A024816 Antisigma(n): Sum of the numbers less than n that do not divide n. 108
 0, 0, 2, 3, 9, 9, 20, 21, 32, 37, 54, 50, 77, 81, 96, 105, 135, 132, 170, 168, 199, 217, 252, 240, 294, 309, 338, 350, 405, 393, 464, 465, 513, 541, 582, 575, 665, 681, 724, 730, 819, 807, 902, 906, 957, 1009, 1080, 1052, 1168, 1182, 1254, 1280, 1377, 1365 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is the sum of proper non-divisors of n, the row sum in triangle A173541. - Omar E. Pol, May 25 2010 LINKS N. J. A. Sloane, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n*(n+1)/2 - sigma(n) = A000217(n) - A000203(n). a(n) = A024916(n-1) - A153485(n), n > 1. - Omar E. Pol, Jun 24 2014 From Wesley Ivan Hurt, Jul 16 2014, Dec 28 2015: (Start) a(n) = Sum_{i=1..n} i * ( ceiling(n/i) - floor(n/i) ). a(n) = Sum_{k=1..n} (n mod k) + (-n mod k). (End) G.f.: x/(1 - x)^3 - Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 18 2017 EXAMPLE a(12)=50 as 5+7+8+9+10+11 = 50 (1,2,3,4,6 not included as they divide 12). MAPLE A024816 := proc(n)     n*(n+1)/2-numtheory[sigma](n) ; end proc: # R. J. Mathar, Aug 03 2013 MATHEMATICA Table[n(n + 1)/2 - DivisorSigma[1, n], {n, 55}] (* Robert G. Wilson v *) Table[Total[Complement[Range[n], Divisors[n]]], {n, 60}] (* Harvey P. Dale, Sep 23 2012 *) With[{nn=60}, #[[1]]-#[[2]]&/@Thread[{Accumulate[Range[nn]], DivisorSigma[ 1, Range[nn]]}]] (* Harvey P. Dale, Nov 22 2014 *) PROG (PARI) a(n)=n*(n+1)/2-sigma(n) \\ Charles R Greathouse IV, Mar 19 2012 (Haskell) a024816 = sum . a173541_row  -- Reinhard Zumkeller, Feb 19 2014 (MAGMA) [n*(n+1) div 2- SumOfDivisors(n): n in [1..60]]; // Vincenzo Librandi, Dec 29 2015 CROSSREFS Cf. A000203 (sigma), A000217, A023896, A024916, A066760, A153485, A173539, A173540, A173541. Sequence in context: A131988 A092593 A231365 * A196443 A007316 A163905 Adjacent sequences:  A024813 A024814 A024815 * A024817 A024818 A024819 KEYWORD easy,nonn,nice AUTHOR Paul Jobling (paul.jobling(AT)whitecross.com) STATUS approved

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Last modified August 26 01:33 EDT 2019. Contains 326324 sequences. (Running on oeis4.)