A062835 -id:A062835 - cp's OEIS frontend

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

Vincenzo Librandi, Jan 01 2014

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

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

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

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

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

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

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

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

Original entry on oeis.org

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

Vincenzo Librandi, Jan 01 2014

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

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

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

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

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

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)

Offset corrected by Amiram Eldar, Dec 09 2024

A234861 Sum of the distinct prime divisors of n^3 - 1.

Original entry on oeis.org

0, 7, 15, 10, 33, 48, 24, 80, 22, 40, 33, 168, 66, 224, 250, 28, 309, 24, 132, 440, 470, 23, 99, 624, 43, 61, 772, 274, 89, 55, 341, 189, 1125, 411, 129, 86, 79, 1520, 251, 563, 1730, 193, 643, 333, 141, 118, 123, 241, 67, 2558, 393, 939, 431, 3024, 97, 150

Offset: 1

Vincenzo Librandi, Jan 01 2014

nonn

			a(3) = 15 because 3^3-1 = 26 and the sum of the 2 distinct prime divisors {2, 13} is 15.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A062835.

Table[Total[Transpose[FactorInteger[n^3 - 1]][[1]]], {n, 50}]

cp's OEIS Frontend

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

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

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Magma

Mathematica

PARI

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A234861 Sum of the distinct prime divisors of n^3 - 1.

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Author

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Examples

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Programs

Mathematica