A229090 - OEIS

%I #14 Oct 02 2020 16:25:34

%S 2,8,10,12,15,16,21,24,30,32,42,44,45,50,52,60,63,64,68,75,76,80,92,

%T 99,105,110,116,117,124,126,128,130,135,136,140,144,147,148,150,152,

%U 153,154,160,164,165,168,170,171,172,182,184,188,189,190,195,198,200

%N Numbers n such that sigma(n) mod n > antisigma(n) mod n, where sigma(n) = A000203(n) = sum of divisors 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 A229089 with respect to A000027, where A229088 = numbers n such that sigma(n) mod n = antisigma(n) mod n, A229089 = numbers n such that sigma(n) mod n < antisigma(n) mod n.

%H Jaroslav Krizek, <a href="/A229090/b229090.txt">Table of n, a(n) for n = 1..10000</a>

%e Number 12 is in sequence because sigma(12) mod 12 = 28 mod 12 = 4 > antisigma(12) mod 12 = 50 mod 12 = 2.

%t smQ[n_]:=Module[{sig=DivisorSigma[1,n]},Mod[sig,n]>Mod[(n(n+1))/2-sig,n]]; Select[Range[200],smQ] (* _Harvey P. Dale_, Dec 23 2013 *)

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

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

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Oct 24 2013