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
KEYWORD
nonn
AUTHOR
STATUS
approved