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A267414 Integers n such that n! = x^3 + y^3 + z^3 where x, y and z are nonnegative integers, is soluble. 0
0, 1, 2, 4, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

0 is a term because 0! = 1 = 0^3 + 0^3 + 1^3.

2 is a term because 2! = 2 = 0^3 + 1^3 + 1^3.

4 is a term because 4! = 24 = 2^3 + 2^3 + 2^3.

From Chai Wah Wu, Jan 18 2016 : (Start)

9! = 36^3 + 52^3 + 56^3

10! = 4^3 + 96^3 + 140^3

11! = 105^3 + 222^3 + 303^3

12! = 35^3 + 309^3 + 766^3

14! = 135^3 + 3153^3 + 3822^3

15! = 1092^3 + 2040^3 + 10908^3

16! = 7644^3 + 21192^3 + 22212^3

17! = 9984^3 + 22848^3 + 69984^3

18! = 18900^3 + 54060^3 + 184080^3

19! = 131040^3 + 331200^3 + 436320^3

20! = 87490^3 + 1034430^3 + 1098440^3

21! = 59850^3 + 2072070^3 + 3481380^3 (End)

MAPLE

isA267414 := proc(n)

    local nf, x, y ;

    nf := n! ;

    for x from 0 do

        if 3*x^3 > nf then

            return false;

        end if;

        for y from x do

            if x^3+2*y^3 > nf then

                break;

            end if;

            if isA000578(nf-x^3-y^3) then

                return true;

            end if;

        end do:

    end do:

end proc:

for n from 0 to 1000 do

    if isA267414(n) then

        print(n) ;

    end if;

end do: # R. J. Mathar, Jan 23 2016

CROSSREFS

Cf. A000142, A000578, A003072, A003325.

Sequence in context: A258710 A246515 A275658 * A072583 A178488 A226821

Adjacent sequences:  A267411 A267412 A267413 * A267415 A267416 A267417

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Jan 14 2016

EXTENSIONS

a(12)-a(16) from Chai Wah Wu, Jan 18 2016

STATUS

approved

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Last modified October 22 21:09 EDT 2018. Contains 316505 sequences. (Running on oeis4.)