login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046763 Numbers n such that the sum of the cubes of the divisors of n is divisible by n. 5
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 (list; graph; refs; listen; history; text; internal format)
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 member. (See the Editorial Comment after the solution to Problem 11090.) - Jonathan Sondow, Nov 23 2012

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

n = 168 = a[ 5 ], Sum[ d^3 ] = 5634720 = 33540*168 = 33540*n or if n = 8128, Sigma[ 3,8128 ] = 613681507712 = 8128*75502154. Moreover 8128 is a perfect number.

MAPLE

with(numtheory);

A046763:=proc(q)

local a, i, n;

for n from 1 to q do

  a:=divisors(n); if frac(add(a[i]^3, i=1..nops(a))/n)=0 then print(n); fi;

od; end:

A046763(100000);  # [Paolo P. Lava, Dec 07 2012]

PROG

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

CROSSREFS

Cf. A007691.

Sequence in context: A256833 A164016 A147811 * A199905 A176780 A169938

Adjacent sequences:  A046760 A046761 A046762 * A046764 A046765 A046766

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 18 22:10 EDT 2017. Contains 290768 sequences.