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A234645
Sum of the divisors of n^3+1.
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
0,2
LINKS
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
EXAMPLE
a(4) = 84 because 4^3+1 = 65 and the sum of the 4 divisors {1, 5, 13, 65} is 84.
MATHEMATICA
Table[Total[Divisors[n^3 + 1]], {n, 0, 50}]
DivisorSigma[1, Range[0, 40]^3+1] (* Harvey P. Dale, Jul 27 2021 *)
PROG
(Magma) [SumOfDivisors(n^3+1): n in [0..50]];
(PARI) a(n) = sigma(n^3+1); \\ Michel Marcus, Jun 19 2015
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 01 2014
STATUS
approved