A261928 a(n) is the number of different pairs (x*y,x+y) mod n.

1, 3, 6, 8, 15, 18, 28, 28, 36, 45, 66, 48, 91, 84, 90, 96, 153, 108, 190, 120, 168, 198, 276, 168, 275, 273, 297, 224, 435, 270, 496, 368, 396, 459, 420, 288, 703, 570, 546, 420, 861, 504, 946, 528, 540, 828, 1128, 576, 1078, 825, 918, 728, 1431, 891, 990, 784, 1140, 1305, 1770, 720, 1891, 1488, 1008, 1408, 1365, 1188, 2278

Offset: 1

Author

Thomas Kerscher, Sep 06 2015

Keywords

• nonn
• mult

Examples

			a(2) = 3 because there exist only the pairs (0,0), (0,1) and (1,0) as results from (x*y,x+y) mod n. There are no x,y with (x*y,x+y)=(1,1) mod 2.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A261929 (number of other pairs).

Programs

PARI

a(n)={my(v=vector(n)); for(i=1, n, for(j=1, n, v[j]=bitor(v[j], 1<<(i*(j-i)%n)))); sum(j=1, n, hammingweight(v[j]))} \\ Andrew Howroyd, Aug 01 2018

Formula

a(n) = n^2 - A261929(n).

Extensions

Keyword:mult added by Andrew Howroyd, Aug 01 2018