A195458 a(n) = floor(sqrt(n)) * a(n-1), starting with 1.

1, 1, 1, 2, 4, 8, 16, 32, 96, 288, 864, 2592, 7776, 23328, 69984, 279936, 1119744, 4478976, 17915904, 71663616, 286654464, 1146617856, 4586471424, 18345885696, 91729428480, 458647142400, 2293235712000, 11466178560000, 57330892800000, 286654464000000

Offset: 1

Author

Peter Luschny, Sep 18 2011

Keywords

• nonn

Comments

a(n) = r(n+2)/sqrt(2); r(1) = sqrt(2); r(n) = r(n-1)/sqrt(n-1) if r(n-1) is a square else r(n) = r(n-1)*floor(sqrt(n-1).

A variation of Recamán's A008336.

Crossrefs

Cf. A008336.

Programs

Maple

r := proc(n) option remember; if n = 1 then sqrt(2)
elif type(r(n-1),square) then r(n-1)/sqrt(n-1)
else r(n-1)*floor(sqrt(n-1)) fi end:
A195458 := proc(n) r(n+2)/sqrt(2) end:

Mathematica

a[1] = 1;
a[n_] := a[n] = Floor[Sqrt[n]] a[n - 1]
Table[a[n], {n, 20}] (* David Callan, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} floor(sqrt(k)). - Ridouane Oudra, Feb 16 2023

Extensions

Better name from David Callan, Aug 14 2013