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A308095 a(n) is the sum of sigma (i.e., A000203) over the totatives of n.

%I A308095 #18 May 13 2019 10:18:59
%S A308095 1,1,4,5,15,7,33,19,40,26,87,27,127,50,84,82,220,59,277,90,187,140,
%T A308095 407,103,401,193,352,207,660,127,762,309,485,339,646,244,1098,423,677,
%U A308095 390,1342,268,1480,525,758,639,1758,416,1666,581,1191,770,2250,527,1742,821,1527,1016,2786,502,3014
%N A308095 a(n) is the sum of sigma (i.e., A000203) over the totatives of n.
%C A308095 a(n) <= A024916(n-1) for n >= 2, with equality if and only if n is prime.
%H A308095 Robert Israel, <a href="/A308095/b308095.txt">Table of n, a(n) for n = 1..10000</a>
%H A308095 Robert Israel, <a href="/A308095/a308095.png">Plot of a(n)/n^2 for 1 <= n <= 20000</a>
%F A308095 a(n) = Sum_{1<=k<=n; gcd(k,n)=1} A000203(k).
%e A308095 a(3) = sigma(1) + sigma(2) = 4.
%p A308095 f:= proc(n) local k; add(numtheory:-sigma(k), k=select(t -> igcd(t,n)=1, [$1..n])) end proc;
%p A308095 map(f, [$1..100]);
%o A308095 (PARI) a(n) = sum(k=1, n, if (gcd(n,k)==1, sigma(k))); \\ _Michel Marcus_, May 13 2019
%Y A308095 Cf. A000203, A024916, A307997.
%K A308095 nonn,look
%O A308095 1,3
%A A308095 _J. M. Bergot_ and _Robert Israel_, May 12 2019