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

Author

Labos Elemer

Keywords

• nonn

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

Examples

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

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.

Crossrefs

Cf. A001158, A007691.

Programs

Mathematica

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

PARI

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