A330866 a(n) = Sum_{d|n, d<n} (n/d) * (n-d).

0, 2, 6, 16, 20, 48, 42, 88, 90, 140, 110, 264, 156, 280, 300, 416, 272, 594, 342, 720, 588, 704, 506, 1248, 700, 988, 972, 1400, 812, 1920, 930, 1824, 1452, 1700, 1540, 2952, 1332, 2128, 2028, 3280, 1640, 3696, 1806, 3432, 3240, 3128, 2162, 5472, 2646, 4350, 3468

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(p^k) = p^k * (p^(k+1) - p*(k+1) + k) / (p-1), where p is prime and k is a positive integer.

a(n) = n*sigma(n) - n*tau(n) = n*A065608(n). - Ridouane Oudra, Apr 11 2024

Example

a(6) = 48; The proper divisors of 6 are 1, 2 and 3. We have (6/1)*(6-1) + (6/2)*(6-2) + (6/3)*(6-3) = 30 + 12 + 6 = 48.

Maple

with(numtheory): seq(n*sigma(n) - n*tau(n), n=1..100); # Ridouane Oudra, Apr 11 2024

Mathematica

Table[Sum[(n/i) (n-i) (1 - Ceiling[n/i] + Floor[n/i]), {i, n-1}], {n, 80}]

Prog

(PARI) a(n)={sumdiv(n, d, (n-d)*n/d)} \\ Andrew Howroyd, Apr 28 2020

Crossrefs

Cf. A000005, A000203, A001065, A065608.

Sequence in context: A082374 A085226 A260376 * A071522 A192532 A379152

Adjacent sequences: A330863 A330864 A330865 * A330867 A330868 A330869

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 28 2020

Status

approved