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

1,4

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.

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A023896, A028491, A066840.

Sequence in context: A346004 A195727 A256701 * A292381 A233655 A307325

Adjacent sequences: A340711 A340712 A340713 * A340715 A340716 A340717

Keyword

nonn,look

Author

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

Status

approved