A226955 Number of representations of n! as a sum of 3 positive cubes.

0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 4, 0, 2, 2, 6, 2, 11, 2, 13, 20, 24, 9

Offset

1,12

Comments

Conjecture: For any t >= 0, there are only finitely many values of n such that a(n) = t. - Altug Alkan, Aug 16 2020

Links

Table of n, a(n) for n=1..23.

Lars Blomberg, Table of n, a(n) for n = 1..21, with solutions

Formula

a(n) = A025456(n!). - Charles R Greathouse IV, Oct 27 2013

Example

n = 12, n! = 479001600 = x^3 + y^3 + z^3 with {x,y,z} = {35,309,766}, {47,214,777}, {60,486,714}, {240,504,696}; 4 solutions, hence a(12) = 4;
n = 16, n! = x^3 + y^3 + z^3 with {x,y,z} = {7644,21192,22212}, {8240,8400,27040}, {10980,15288,25212}, {11648,18016,23808}, {12096,19968,22368}, {13030,18330,23240}; 6 solutions, hence a(16) = 6.
From Chai Wah Wu, May 21 2017: (Start)
n = 22, n! = x^3 + y^3 + z^3 with (x,y,z) = (286272, 8168832, 8334144), (443100, 4806340, 10042760), (663040, 7882560, 8590400), (720720, 5343408, 9902592), (757890, 8108100, 8389710), (854812, 2888886, 10320506), (861120, 3584160, 10251360), (1025640, 2784600, 10326960), (1266408, 4510296, 10099728), (1443806, 7114569, 9129295), (1792350, 6013602, 9657648), (1814400, 3689280, 10221120), (1871415, 4292190, 10126305), (1926720, 5685120, 9771840), (2419200, 7506240, 8823360), (2517424, 7223832, 9008552), (2779200, 3144960, 10232640), (2870532, 6957468, 9140040), (3021408, 4549080, 10007592), (3244410, 7888800, 8429190), (3776535, 6384105, 9321480), (5083936, 5242592, 9467136), (5681592, 7233408, 8253000), (6391665, 6719895, 8239770)
n = 23, n! = x^3 + y^3 + z^3 with (x,y,z) = (136080, 8250480, 29352960), (5369910, 6098890, 29422400), (5766592, 18082176, 27029696), (6151320, 19606860, 26247060), (7572485, 23185155, 23485930), (8255520, 10856160, 28848960), (8678304, 19104696, 26316360), (11959740, 19850400, 25365060), (13799880, 22091640, 23172240)
(End)

Crossrefs

Cf. A003072 (numbers that are the sum of 3 positive cubes), A267414.

Sequence in context: A218769 A180850 A109157 * A123314 A058997 A261164

Adjacent sequences: A226952 A226953 A226954 * A226956 A226957 A226958

Keyword

nonn,more

Author

Zak Seidov, Jun 26 2013

Extensions

a(17)-a(18) from Giovanni Resta, Jun 26 2013

a(4) corrected and a(19)-a(21) from Lars Blomberg, Sep 07 2013

a(22)-a(23) from Chai Wah Wu, May 21 2017

Status

approved