A085599 Number of pairs of coprimes (n-i,n+i), 1

0, 0, 1, 1, 2, 1, 3, 3, 3, 3, 5, 3, 6, 5, 4, 7, 8, 5, 9, 7, 6, 9, 11, 7, 10, 11, 9, 11, 14, 7, 15, 15, 10, 15, 12, 11, 18, 17, 12, 15, 20, 11, 21, 19, 12, 21, 23, 15, 21, 19, 16, 23, 26, 17, 20, 23, 18, 27, 29, 15, 30, 29, 18, 31, 24, 19, 33, 31, 22, 23, 35, 23, 36, 35, 20

Offset: 1

Author

Reinhard Zumkeller, Jul 06 2003

Keywords

• nonn

Examples

			n=7: (7-2,7+2)=(5,9), (7-3,7+3)=(4,10), (7-4,7+4)=(3,11), (7-5,7+5)=(2,12), (7-6,7+6)=(1,13): only three are coprime: (5,9), (3,11) and (1,13), therefore a(7)=3.
		

Crossrefs

Cf. A055034, A102781.

Programs

Maple

A085599 := proc(n)
    local i,a;
    a := 0 ;
    for i from 2 to n-1 do
        if igcd(n-i,n+i) = 1 then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Jul 09 2016

Formula

For n>1, a(n) = A055034(n) - ((-1)^n + 1)/2 = A000010(2*n)/2 - ((-1)^n + 1)/2. - Max Alekseyev, Jul 21 2016

Extensions

Definition corrected by Ray Chandler, Jul 09 2016