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A024816 Antisigma(n): Sum of the numbers less than n that do not divide n. 107
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)

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 July 24 21:38 EDT 2017. Contains 289777 sequences.