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Hexagonal numbers that are products of smaller hexagonal numbers.
2

%I #7 Jul 07 2024 13:51:26

%S 1,2850,61776,79800,103740,145530,437580,719400,810901,828828,1050525,

%T 1185030,1788886,2031120,2162160,2821500,4250070,4959675,9217071,

%U 12298320,12457536,16356340,22899528,23334696,24890040,30728880,32800950,45158256,48565440,58487520

%N Hexagonal numbers that are products of smaller hexagonal numbers.

%C There are infinitely many terms where the corresponding product has two factors. This can be proved by solving a certain generalized Pell equation, as in A374372.

%e 1 is a term because it is a hexagonal number and equals the empty product.

%e 2850 is a term because it is a hexagonal number and equals the product of the hexagonal numbers 15 and 190.

%e 103740 is a term because it is a hexagonal number and equals the product of the hexagonal numbers 6, 91, and 190. (This is the first term that requires more than two factors.)

%Y Row n=6 of A374370.

%Y Cf. A000384, A374372.

%K nonn

%O 1,2

%A _Pontus von Brömssen_, Jul 07 2024