%I #19 Jan 18 2021 04:35:45

%S 0,0,1,2,4,4,9,8,13,12,25,12,36,24,32,32,64,28,81,40,66,60,121,48,124,

%T 84,121,84,196,56,225,128,170,144,216,108,324,180,240,160,400,120,441,

%U 220,272,264,529,192,513,252,416,312,676,244,560,336,522,420,841,240,900,480,570,512,792,320

%N a(n) is the sum of (n-2*j) for j < n/2 coprime to n.

%C Sum of differences j-i for 0 < i < j coprime to n with i+j = n.

%C If p is an odd prime, a(p^k) = (p-1)*(p^(2*k-1)-1)/4.

%C Primes in this sequence are a(4) = 2 and a(3^k) = (3^(2*k-1)-1)/2 where 2*k-1 is in A028491.

%H Robert Israel, <a href="/A340714/b340714.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A023896(n) - 2*A066840(n) for n >= 3.

%F a(n) = Sum_{k=1..floor((n-1)/2)} floor(1/gcd(n,n-k)) * (n-2*k). - _Wesley Ivan Hurt_, Jan 18 2021

%e For n = 10, a(10) = (10-2*1) + (10-2*3) = 12.

%p f:= proc(n) local j; add(n-2*j, j= select(t -> igcd(t,n)=1, [$1..(n-1)/2])) end proc:

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

%t Table[Sum[(n - 2 i) Floor[1/GCD[n - i, n]], {i, Floor[(n-1)/2]}], {n, 80}] (* _Wesley Ivan Hurt_, Jan 18 2021 *)

%Y Cf. A023896, A028491, A066840.

%K nonn,look

%O 1,4

%A _J. M. Bergot_ and _Robert Israel_, Jan 17 2021