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A340180 a(n) = Sum_{x in C(n)} (sigma(n) mod x), where C(n) is the set of numbers < n coprime to n, and sigma = A000203.

%I A340180 #18 Feb 03 2021 23:40:36
%S A340180 0,0,0,1,2,2,7,1,16,4,16,9,30,23,26,24,46,19,60,30,60,52,84,43,132,77,
%T A340180 105,62,137,51,166,88,183,139,182,117,247,186,239,158,283,99,327,194,
%U A340180 259,284,373,176,462,234,442,294,491,235,508,294,514,430,585,259,671,519,546,408,749,323,798
%N A340180 a(n) = Sum_{x in C(n)} (sigma(n) mod x), where C(n) is the set of numbers < n coprime to n, and sigma = A000203.
%H A340180 Robert Israel, <a href="/A340180/b340180.txt">Table of n, a(n) for n = 1..10000</a>
%e A340180 For n=8, sigma(8) = 15 and C(8) = {1,3,5,7} so a(8) = (15 mod 1) + (15 mod 3) + (15 mod 5) + (15 mod 7) = 1.
%p A340180 f := proc(n) local C,s,c;
%p A340180   s:= numtheory:-sigma(n);
%p A340180   C:=select(t -> igcd(t,n) = 1, [$1..n-1]);
%p A340180   add(s mod c, c=C)
%p A340180 end proc:
%p A340180 map(f, [$1..100]);
%t A340180 Table[Sum[Mod[DivisorSigma[1, n], k] Floor[1/GCD[k, n]], {k, n - 1}], {n, 80}] (* _Wesley Ivan Hurt_, Jan 30 2021 *)
%o A340180 (PARI) a(n) = my(s=sigma(n)); sum(k=1, n, if (gcd(k, n)==1, s % k)); \\ _Michel Marcus_, Jan 31 2021
%Y A340180 Cf. A000203, A340179, A337189 (n | a(n)).
%K A340180 nonn,look
%O A340180 1,5
%A A340180 _J. M. Bergot_ and _Robert Israel_, Dec 30 2020