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

1,2

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A261929 (number of other pairs).

Sequence in context: A274605 A213983 A174133 * A246141 A051212 A143869

Adjacent sequences: A261925 A261926 A261927 * A261929 A261930 A261931

Keyword

nonn,mult

Author

Thomas Kerscher, Sep 06 2015

Extensions

Keyword:mult added by Andrew Howroyd, Aug 01 2018

Status

approved