A318937 a(n) = 16 times the sum of the cubes of the divisors of 2*n+1.
16, 448, 2016, 5504, 12112, 21312, 35168, 56448, 78624, 109760, 154112, 194688, 252016, 327040, 390240, 476672, 596736, 693504, 810464, 984704, 1102752, 1272128, 1526112, 1661184, 1887888, 2201472, 2382048, 2685312, 3073280, 3286080, 3631712, 4166528, 4431168, 4812224
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..5000
- P. J. C. Lamont, The number of Cayley integers of given norm, Proceedings of the Edinburgh Mathematical Society, 25.1 (1982): 101-103. See (6).
Programs
-
Magma
[16*DivisorSigma(3, 2*n+1): n in [0..40]]; // Vincenzo Librandi, Sep 16 2018
-
Maple
with(numtheory); rJ0 := proc(k) local n,d; n:=2*k+1; 16*add(d^3, d in divisors(n)); end; [seq(rJ0(k),k=0..60)];
-
Mathematica
16 DivisorSigma[3, Range[1, 75, 2]] (* Vincenzo Librandi, Sep 16 2018 *)
Formula
Sum_{k=0..n} a(k) ~ 30*zeta(4) * n^4. - Amiram Eldar, Dec 12 2023