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
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