A067817 a(n) = Sum_{r|n, s|n, t|n, r<s<t} r*s*t.

0, 0, 0, 8, 0, 72, 0, 120, 27, 180, 0, 1400, 0, 336, 360, 1240, 0, 3285, 0, 3948, 672, 792, 0, 15960, 125, 1092, 1080, 8240, 0, 25992, 0, 11160, 1584, 1836, 1680, 57065, 0, 2280, 2184, 46620, 0, 56352, 0, 23592, 18612, 3312, 0, 150040, 343, 29955, 3672

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

(1/3!)*(sigma[1](n)^3-3*sigma[1](n)*sigma[2](n)+2*sigma[3](n)).

Maple

a:= n-> coeff(expand(mul(1+d*x, d=numtheory[divisors](n))), x, 3):
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 18 2023

Prog

(PARI) a(n) = 1/6*(sigma(n, 1)^3 - 3*sigma(n, 1)*sigma(n, 2) + 2*sigma(n, 3)) \\ Michel Marcus, Jun 17 2013

Crossrefs

Cf. A067692, A068020, A000203, A001157, A001158.

Column k=3 of A224381.

Sequence in context: A270006 A167318 A186979 * A350452 A079137 A181689

Adjacent sequences: A067814 A067815 A067816 * A067818 A067819 A067820

Keyword

nonn

Author

Vladeta Jovovic, Feb 08 2002

Status

approved