A046763 Numbers that divide the sum of cubes of their divisors.

1, 6, 42, 120, 168, 270, 280, 312, 496, 672, 728, 840, 1080, 1560, 1782, 1806, 1890, 2044, 2184, 2520, 3472, 3640, 3913, 4256, 5880, 6048, 6552, 6615, 7224, 7560, 7826, 8128, 9120, 9424, 9933, 10804, 10920, 11400, 12040, 12768, 13230, 13626, 14040

Offset

1,2

Comments

Compare with multiply perfect numbers, A007691. Here Sum(divisors) is replaced by Sum(cube of divisors).

Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006

Tomohiro Yamada found that the odd number 209195 is a term. (See the Editorial Comment after the solution to Problem 11090.) - Jonathan Sondow, Nov 23 2012

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373.

Example

For k = 168 = a(5), Sum(d^3) = 5634720 = 33540*168 = 33540*k;

Mathematica

Select[Range[10^4], Divisible[DivisorSigma[3, #], #] &] (* Amiram Eldar, Sep 10 2019 *)

Prog

(PARI) is(n)=sigma(n, 3)%n==0 \\ Charles R Greathouse IV, Feb 04 2013

Crossrefs

Cf. A001158, A007691.

Sequence in context: A256833 A164016 A147811 * A199905 A360757 A176780

Adjacent sequences: A046760 A046761 A046762 * A046764 A046765 A046766

Keyword

nonn

Author

Labos Elemer

Status

approved