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A242480 a(n) = (n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n.

%I A242480 #9 Sep 08 2022 08:46:08
%S A242480 0,2,3,8,5,6,7,16,9,20,11,12,13,28,15,32,17,18,19,20,21,44,23,24,25,
%T A242480 52,27,28,29,30,31,64,33,68,35,72,37,76,39,40,41,42,43,88,45,92,47,96,
%U A242480 49,100,51,104,53,54,55,56,57,116,59,120,61,124,63,128,65,66
%N A242480 a(n) = (n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n.
%C A242480 a(n) / n = 1 for numbers n from A242482, a(n) / n = 2 for numbers n from A242483.
%C A242480 If there are any odd multiply-perfect numbers n > 1 then a(n) = 0.
%C A242480 Possible values of a(n) in increasing order = A242485. Numbers m such that a(n) = m has no solution = A242486.
%H A242480 Jaroslav Krizek, <a href="/A242480/b242480.txt">Table of n, a(n) for n = 1..10000</a>
%F A242480 a(n) = A142150(n) + A054024(n) + A229110(n) = (A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n).
%F A242480 a(n) = A242481(n) * n.
%e A242480 a(8) = (8*(8+1)/2) mod 8 + sigma(8) mod 8 + antisigma(8) mod 8 = 36 mod 8 + 15 mod 8 + 21 mod 8 = 4 + 7 + 5 = 16.
%o A242480 (Magma) [((n*(n+1)div 2 mod n + SumOfDivisors(n) mod n + (n*(n+1)div 2-SumOfDivisors(n)) mod n)): n in [1..1000]]
%Y A242480 Cf. A242481, A242482, A242483, A242484, A242485, A242486.
%K A242480 nonn
%O A242480 1,2
%A A242480 _Jaroslav Krizek_, May 16 2014