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a(n) = Sum_{i+j<=m+1} t_i * t_j, where t_1 < ... < t_m are the totatives of n.
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%I #15 Feb 09 2021 02:46:15

%S 1,1,5,7,35,11,126,70,177,90,715,142,1365,357,680,876,3876,645,5985,

%T 1300,2856,2255,12650,1916,11675,4446,11061,5362,31465,3260,40920,

%U 12376,18920,13192,30240,9066,82251,20691,37752,19080,123410,13062,148995,34870,52080,44781,211876,27640,186102,45650

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

%C The totatives of n are the numbers k <= n with gcd(k,n) = 1.

%C If p is prime, a(p) = (p+2)*(p+1)*p*(p-1)/24.

%C It appears that 12*a(n) is always a multiple of n.

%C 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 Robert Israel, <a href="/A341063/b341063.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 f:= proc(n) local C,i,S,t;

%p C:= select(t -> igcd(t,n)=1, [$1..n]);

%p S:= ListTools:-PartialSums(C);

%p add(S[-i]*C[i], i=1..nops(C))

%p end proc:

%p map(f, [$1..100]);

%Y Cf. A038566.

%K nonn

%O 1,3

%A _J. M. Bergot_ and _Robert Israel_, Feb 04 2021