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%I #6 Sep 08 2022 08:46:08
%S 0,1,1,2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,2,
%T 1,2,1,2,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,2,1,2,1,2,1,2,1,1,1,2,
%U 1,1,1,2,1,2,1,2,1,1,1,1,1,2,1,2,1,2,1
%N a(n) = ((n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n) / n.
%C a(1) = 0. If there is no odd multiply-perfect number then a(n) = 1 or 2 for n >= 2. See A242482 = numbers m such that a(n) = 1, A242483 = numbers m such that a(n) = 2. If there are any odd multiply-perfect numbers m > 1 then a(m) = 0.
%H Jaroslav Krizek, <a href="/A242481/b242481.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A142150(n) + A054024(n) + A229110(n)) / n = ((A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n)) / n.
%F a(n) = A242480(n) / n.
%e a(8) = [(8*(8+1)/2) mod 8 + sigma(8) mod 8 + antisigma(8) mod 8] / 8 = (36 mod 8 + 15 mod 8 + 21 mod 8) / 8 = (4 + 7 + 5 ) / 8 = 2.
%o (Magma) [((n*(n+1)div 2 mod n + SumOfDivisors(n) mod n + (n*(n+1)div 2-SumOfDivisors(n)) mod n))div n: n in [1..1000]]
%Y Cf. A242480, A242482, A242483, A242484, A242485, A242486.
%K nonn
%O 1,4
%A _Jaroslav Krizek_, May 16 2014
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