A234860 Sum of the divisors of n^3 - 1.

8, 42, 104, 224, 264, 780, 592, 1680, 1520, 2880, 1896, 5642, 2968, 5808, 8736, 9548, 7200, 15360, 8440, 19488, 19032, 23040, 14448, 49920, 23560, 31836, 32912, 53312, 34200, 77688, 38912, 70812, 62088, 74088, 67584, 152320, 56392, 107520, 99736

Offset: 2

Author

Vincenzo Librandi, Jan 01 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..1001

Crossrefs

Cf. A000203, A062835, A065764, A068601, A175926, A193433, A333240.

Programs

Magma

[SumOfDivisors(n^3-1): n in [2..50]];

Mathematica

Table[Total[Divisors[n^3 - 1]], {n, 2, 50}]

PARI

a(n) = sigma(n^3-1); \\ Amiram Eldar, Dec 09 2024

Formula

From Amiram Eldar, Dec 09 2024: (Start)

a(n) = A000203(A068601(n)).

Sum_{k=2..n} a(k) = c * n^4 + O((n*log(n))^3), where c = (83/288) * Product_{primes p == 1 (mod 3)} ((p^2+2)/(p^2-1)) * Product_{primes p == 2 (mod 3)} (p^2/(p^2-1)) = 0.4499262799... . (End)

Extensions

Offset corrected by Amiram Eldar, Dec 09 2024