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A341063 a(n) = Sum_{i+j<=m+1} t_i * t_j, where t_1 < ... < t_m are the totatives of n.

%I A341063 #15 Feb 09 2021 02:46:15
%S A341063 1,1,5,7,35,11,126,70,177,90,715,142,1365,357,680,876,3876,645,5985,
%T A341063 1300,2856,2255,12650,1916,11675,4446,11061,5362,31465,3260,40920,
%U A341063 12376,18920,13192,30240,9066,82251,20691,37752,19080,123410,13062,148995,34870,52080,44781,211876,27640,186102,45650
%N A341063 a(n) = Sum_{i+j<=m+1} t_i * t_j, where t_1 < ... < t_m are the totatives of n.
%C A341063 The totatives of n are the numbers k <= n with gcd(k,n) = 1.
%C A341063 If p is prime, a(p) = (p+2)*(p+1)*p*(p-1)/24.
%C A341063 It appears that 12*a(n) is always a multiple of n.
%C A341063 Conjecture: if p and q are distinct primes, a(p*q) = (p^2-p)*(q^2-q)*(p^2*q^2-p^2*q-p*q^2+p*q+2*p+2*q)/24.
%H A341063 Robert Israel, <a href="/A341063/b341063.txt">Table of n, a(n) for n = 1..10000</a>
%e A341063 The totatives of 8 are 1, 3, 5, 7, so a(8) = 1*(1+3+5+7)+3*(1+3+5)+5*(1+3)+7*1 = 70.
%p A341063 f:= proc(n) local C,i,S,t;
%p A341063   C:= select(t -> igcd(t,n)=1, [$1..n]);
%p A341063   S:= ListTools:-PartialSums(C);
%p A341063   add(S[-i]*C[i], i=1..nops(C))
%p A341063 end proc:
%p A341063 map(f, [$1..100]);
%Y A341063 Cf. A038566.
%K A341063 nonn
%O A341063 1,3
%A A341063 _J. M. Bergot_ and _Robert Israel_, Feb 04 2021