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Smallest number that is the difference between two positive cubes in n ways.
2

%I #9 Mar 19 2020 07:43:56

%S 7,721,3367,4118877,1412774811,424910390480793

%N Smallest number that is the difference between two positive cubes in n ways.

%C a(7) <= 15490327057569000, a(8) <= 123922616460552000. - _Giovanni Resta_, Mar 19 2020

%e Pairs (x, y) such that x^3 - y^3 = a(1), ..., a(6):

%e 7 = (2, 1);

%e 721 = (16, 15), (9, 2);

%e 3367 = (34, 33), (16, 9), (15, 2)l

%e 4118877 = (162, 51), (165, 72), (178, 115), (678, 675);

%e 1412774811 = (1134, 357), (1155, 504), (1246, 805), (2115, 2004), (4746, 4725);

%e 424910390480793 = (596001, 595602), (317982, 316575), (141705, 134268), (83482, 53935), (77385, 33768), (75978, 23919).

%Y Cf. A014439, A014440, A014441, A181123, A034179, A265625, A333376, A333377.

%Y Cf. A011541,A047696.

%K nonn,hard,more

%O 1,1

%A _Jeff Burch_, Sep 23 2004

%E a(6) from _Giovanni Resta_, Mar 19 2020