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A024816
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Antisigma(n): Sum of the numbers less than n that do not divide n.
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116
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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
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OFFSET
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1,3
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COMMENTS
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a(n) is the sum of proper non-divisors of n, the row sum in triangle A173541. - Omar E. Pol, May 25 2010
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LINKS
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FORMULA
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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
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EXAMPLE
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a(12)=50 as 5+7+8+9+10+11 = 50 (1,2,3,4,6 not included as they divide 12).
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MAPLE
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n*(n+1)/2-numtheory[sigma](n) ;
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
(Magma) [n*(n+1) div 2- SumOfDivisors(n): n in [1..60]]; // Vincenzo Librandi, Dec 29 2015
(Python)
from sympy import divisor_sigma
(SageMath)
def A024816(n): return sum(k for k in (0..n-1) if not k.divides(n))
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CROSSREFS
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Cf. A000203 (sigma), A000217, A004125, A023896, A024916, A066760, A076617, A153485, A173539, A173540, A173541, A244048, A352810, A352811.
Cf. A342344 (for a symmetric representation).
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Paul Jobling (paul.jobling(AT)whitecross.com)
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STATUS
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approved
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