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A281626 a(n) = (sum of trivial divisors of n) - (sum of nontrivial divisors of n).

%I A281626 #18 Jul 26 2025 17:26:22
%S A281626 1,3,4,3,6,2,8,3,7,4,12,-2,14,6,8,3,18,-1,20,0,12,10,24,-10,21,12,16,
%T A281626 2,30,-10,32,3,20,16,24,-17,38,18,24,-8,42,-10,44,6,14,22,48,-26,43,9,
%U A281626 32,8,54,-10,40,-6,36,28,60,-46,62,30,24,3,48,-10,68,12
%N A281626 a(n) = (sum of trivial divisors of n) - (sum of nontrivial divisors of n).
%C A281626 Trivial divisors of n are numbers 1 and n.
%C A281626 a(n) = 0 for numbers in A088831 (numbers n whose abundance is 2).
%C A281626 a(n) <= 0 for numbers in A005101 (abundant numbers).
%C A281626 a(n) > 0 for numbers in A263837 (non-abundant numbers).
%H A281626 Indranil Ghosh, <a href="/A281626/b281626.txt">Table of n, a(n) for n = 1..10000</a>
%F A281626 a(1) = 1; for n>1, a(n) = (n+1) - (sigma(n) - n - 1) = 2*(n+1) - sigma(n) = n + 1 - A048050(n).
%F A281626 a(A000396(n)) = 2 for n >= 1.
%F A281626 a(A000079(n)) = 3 for n >= 1.
%F A281626 a(A006881(n)) = phi(n).
%F A281626 a(p) = p + 1 for p prime.
%e A281626 a(20) = (20+1) - (2+4+5+10) = 0.
%t A281626 Table[If[n == 1, 1, 2 (n + 1) - DivisorSigma[1, n]], {n, 68}] (* _Michael De Vlieger_, Feb 11 2017 *)
%o A281626 (Magma) [1] cat [2*(n+1) - SumOfDivisors(n): n in [2..100]];
%Y A281626 Cf. A000079, A000396, A005101, A006881, A048050, A088831, A263837.
%K A281626 sign
%O A281626 1,2
%A A281626 _Jaroslav Krizek_, Feb 11 2017