A340714 a(n) is the sum of (n-2*j) for j < n/2 coprime to n.

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, 84, 121, 84, 196, 56, 225, 128, 170, 144, 216, 108, 324, 180, 240, 160, 400, 120, 441, 220, 272, 264, 529, 192, 513, 252, 416, 312, 676, 244, 560, 336, 522, 420, 841, 240, 900, 480, 570, 512, 792, 320

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 17 2021

Keywords

• nonn
• look

Comments

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

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

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.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023896, A028491, A066840.

Programs

Maple

f:= proc(n) local j; add(n-2*j, j= select(t -> igcd(t,n)=1, [$1..(n-1)/2])) end proc:
map(f, [$1..100]);

Mathematica

Table[Sum[(n - 2 i) Floor[1/GCD[n - i, n]], {i, Floor[(n-1)/2]}], {n, 80}] (* Wesley Ivan Hurt, Jan 18 2021 *)

Formula

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

a(n) = Sum_{k=1..floor((n-1)/2)} floor(1/gcd(n,n-k)) * (n-2*k). - Wesley Ivan Hurt, Jan 18 2021