A234645 Sum of the divisors of n^3+1.

1, 3, 13, 56, 84, 312, 256, 660, 800, 1332, 1344, 3458, 2240, 3792, 4836, 6572, 4356, 13440, 6160, 16800, 13312, 15192, 11136, 35685, 19840, 25284, 30976, 42560, 22740, 63648, 30464, 71820, 51792, 65664, 53952, 111440, 52136, 84480, 99008, 133560, 75264

Offset: 0

Author

Vincenzo Librandi, Jan 01 2014

Keywords

• nonn
• easy

Examples

			a(4) = 84 because 4^3+1 = 65 and the sum of the 4 divisors {1, 5, 13, 65} is 84.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000203, A001093, A062835, A065764, A175926, A193433, A333240.

Programs

Magma

[SumOfDivisors(n^3+1): n in [0..50]];

Mathematica

Table[Total[Divisors[n^3 + 1]], {n, 0, 50}]
DivisorSigma[1,Range[0,40]^3+1] (* Harvey P. Dale, Jul 27 2021 *)

PARI

a(n) = sigma(n^3+1); \\ Michel Marcus, Jun 19 2015

Formula

a(n) = A000203(A001093(n)). - Michel Marcus, Jun 19 2015

Sum_{k=1..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)) = 0.449926279... . - Amiram Eldar, Dec 09 2024