login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274132 Numbers n such that n^k is the sum of three positive cubes for all positive integers k. 0
134, 153, 216, 225, 244, 251, 288, 342, 368, 405, 408, 415, 528, 532, 540, 577, 645, 729, 750, 755, 764, 855, 863, 882, 918, 919, 946, 972, 980, 1065, 1072, 1080, 1126, 1224, 1250, 1333, 1351, 1422, 1457, 1464, 1466, 1520, 1539, 1548, 1581, 1611, 1701, 1728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Cubes in this sequence are 216, 729, 1728, 5832, 6859, ...

If n, n^2 and n^3 are sums of three positive cubes, then n is in the sequence, because if n^k = a^3 + b^3 + c^3, n^(3+k) = (na)^3 + (nb)^3 + (nc)^3. - Robert Israel, Jul 02 2019

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

134 is a term because 134 = 1^3 + 2^3 + 5^3, 134^2 = 10^3 + 11^3 + 25^3, 134^3 = 44^3 + 102^3 + 108^3, 134^4 = 134^3 + (2*134)^3 + (5*134)^3, 134^5 = 1340^3 + (11*134)^3 + (25*134)^3, ...

MAPLE

A3072:= proc(n) local a, b, c;

  for a from 1 while 3*a^3<=n do

   for b from a while a^3 + 2*b^3 <= n do

     c:= floor((n-a^3-b^3)^(1/3));

     if a^3+b^3+c^3=n then return true fi;

od od;

false

end proc:

filter:= n -> A3072(n) and A3072(n^2) and A3072(n^3):

select(filter, [$1..2000]); # Robert Israel, Jul 02 2019

CROSSREFS

Cf. A003072.

Sequence in context: A191715 A208626 A061491 * A252133 A255795 A048128

Adjacent sequences:  A274129 A274130 A274131 * A274133 A274134 A274135

KEYWORD

nonn

AUTHOR

Altug Alkan, Jun 10 2016

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)