A372509 Numbers that can be written as a product of double factorials of odd numbers.

1, 3, 9, 15, 27, 45, 81, 105, 135, 225, 243, 315, 405, 675, 729, 945, 1215, 1575, 2025, 2187, 2835, 3375, 3645, 4725, 6075, 6561, 8505, 10125, 10395, 10935, 11025, 14175, 18225, 19683, 23625, 25515, 30375, 31185, 32805, 33075, 42525, 50625

Offset: 1

Author

Ilya Gutkovskiy, May 04 2024

Keywords

• nonn

Crossrefs

Cf. A001013, A001147, A025487, A057863.

Programs

Mathematica

kmax = 60000;
maxExponent = 10;
ff = Select[TakeWhile[Range[3, kmax], #!! < kmax &]!!, OddQ];
lg = Length@ff;
iter = Sequence @@ Table[{x[i], 0, maxExponent}, {i, 1, lg}];
seq = Table[k = Times @@ Table[ff[[i]]^x[i] , {i, 1, lg}]; If[k <= kmax, k, Nothing], Evaluate@iter] // Flatten // Union (* Jean-François Alcover, May 11 2024 *)