A229089 - OEIS

%I #17 Jan 24 2022 12:49:40

%S 3,5,6,7,9,11,13,14,17,18,19,20,22,23,25,26,27,28,29,31,33,34,35,36,

%T 37,38,39,41,43,46,47,48,49,51,53,54,55,56,57,58,59,61,62,65,66,67,69,

%U 70,71,72,73,74,77,78,79,81,82,83,84,85,86,87,88,89,90,91,93

%N Numbers n such that sigma(n) mod n < antisigma(n) mod n, where sigma(n) = A000203(n) = sum of divisor of n, antisigma(n) = A024816(n) = sum of non-divisors of n.

%C Numbers n such that A229087(n) = A000203(n) mod n - A024816(n) mod n =A054024(n) - A229110(n) < 0.

%C Complement of union A229088 and A229090 with respect to A000027, where

%C A229088 = numbers n such that sigma(n) mod n = antisigma(n) mod n,

%C A229090 = numbers n such that sigma(n) mod n > antisigma(n) mod n.

%H Jaroslav Krizek, <a href="/A229089/b229089.txt">Table of n, a(n) for n = 1..10000</a>

%e Number 11 is in sequence because sigma(11) mod 11 = 12 mod 11 = 1 < antisigma(11) mod 11 = 54 mod 11 = 10.

%t Select[Range[100],Mod[Total[Complement[Range[#],Divisors[#]]],#]> Mod[ DivisorSigma[ 1,#],#]&] (* _Harvey P. Dale_, Jan 24 2022 *)

%Y Cf. A000203 (sigma(n)), A024816 (antisigma(n)), A229110 (antisigma(n) mod n), A054024 (sigma(n) mod n).

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Oct 24 2013