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%I #53 Sep 08 2022 08:46:06
%S 0,0,1,0,3,-1,5,0,4,1,9,-5,11,3,5,0,15,-4,17,-3,9,7,21,-13,18,9,13,-1,
%T 27,-13,29,0,17,13,21,-20,35,15,21,-11,39,-13,41,3,11,19,45,-29,40,6,
%U 29,5,51,-13,37,-9,33,25,57,-49,59,27,21,0,45,-13,65,9,41
%N 2*n - 1 - sigma(n).
%C Partial sums give A004125.
%C Also 0 together with A120444.
%C It appears that a(n) = 0 iff n is a power of 2.
%C Numbers n with a(n) = 0 are called "almost perfect", "least deficient" or "slightly defective" numbers. See A000079. - _Robert Israel_, Jul 22 2014
%C a(n) = n - 2 iff n is prime.
%C a(n) = -1 iff n is a perfect number.
%C Also the alternating row sums of A239446. - _Omar E. Pol_, Jul 21 2014
%D R. K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, New York, 2004.
%H T. D. Noe, <a href="/A235796/b235796.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A005408(n-1) - A000203(n).
%F a(n) = -1 - A033880(n). - _Michel Marcus_, Jan 27 2014
%F a(n) = n - 1 - A001065(n). - _Omar E. Pol_, Jan 29 2014
%F a(n) = A033879(n) - 1. - _Omar E. Pol_, Jan 30 2014
%F a(n) = 2*n - 2 - A039653(n). - _Omar E. Pol_, Jan 31 2014
%F a(n) = (-1)*A237588(n). - _Omar E. Pol_, Feb 23 2014
%F a(n) = 2*n - A088580(n). - _Omar E. Pol_, Mar 23 2014
%e . The positive The sum of
%e n odd numbers divisors of n. a(n)
%e 1 1 1 0
%e 2 3 3 0
%e 3 5 4 1
%e 4 7 7 0
%e 5 9 6 3
%e 6 11 12 -1
%e 7 13 8 5
%e 8 15 15 0
%e 9 17 13 4
%e 10 19 18 1
%e ...
%t Table[2n-1-DivisorSigma[1,n],{n,70}] (* _Harvey P. Dale_, Jul 11 2014 *)
%o (PARI) vector(100, n, (2*n-1)-sigma(n)) \\ _Colin Barker_, Jan 27 2014
%o (Magma) [2*n-1-SumOfDivisors(n): n in [1..100]]; // _Vincenzo Librandi_, Feb 25 2014
%Y Cf. A000079, A000203, A000396, A004125, A005408, A120444, A196020, A236104.
%K sign
%O 1,5
%A _Omar E. Pol_, Jan 25 2014
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