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
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
From Omar E. Pol, Mar 21 2021: (Start)
a(p) = (p-2)*(p+1)/2 for p prime. - Bernard Schott, Apr 12 2022
EXAMPLE
a(12)=50 as 5+7+8+9+10+11 = 50 (1,2,3,4,6 not included as they divide 12).
MAPLE
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
(Python)
from sympy import divisor_sigma
def A024816(n): return (n*(n+1)>>1)-divisor_sigma(n) # Chai Wah Wu, Apr 28 2023
(SageMath)
def A024816(n): return sum(k for k in (0..n-1) if not k.divides(n))
print([A024816(n) for n in srange(1, 55)]) # Peter Luschny, Nov 14 2023
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
Paul Jobling (paul.jobling(AT)whitecross.com)
STATUS
approved