|
|
A331761
|
|
a(n) = Sum_{i=1..n, j=1..n, gcd(i,j)=2} (n+1-i)*(n+1-j).
|
|
8
|
|
|
0, 1, 4, 15, 32, 71, 124, 211, 320, 499, 716, 999, 1328, 1799, 2340, 3023, 3792, 4767, 5852, 7135, 8544, 10319, 12260, 14471, 16864, 19775, 22916, 26467, 30272, 34587, 39188, 44347, 49824, 56195, 62948, 70311, 78080, 86975
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
Conjecture: As n -> oo, a(n) ~ C*n^4/Pi^2, where C is about 0.3775. - N. J. A. Sloane, Jul 03 2020
a(n) = (n-1)^2 + 2*Sum_{i=2..floor(n/2)} (n+1-2*i)*(n+1-i)*phi(i). - Chai Wah Wu, Aug 16 2021
|
|
MATHEMATICA
|
Table[Sum[Boole[GCD[i, j] == 2] (n + 1 - i) (n + 1 - j), {i, n}, {j, n}], {n, 38}] (* Michael De Vlieger, Feb 04 2020 *)
|
|
PROG
|
(Python)
from sympy import totient
def A331761(n): return (n-1)**2 + 2*sum(totient(i)*(n+1-2*i)*(n+1-i) for i in range(2, n//2+1)) # Chai Wah Wu, Aug 16 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|