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

1,4

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.

Links

Table of n, a(n) for n=1..30.

Formula

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

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 *)

Crossrefs

Cf. A008336.

Sequence in context: A290555 A035523 A290301 * A264656 A078227 A250073

Adjacent sequences: A195455 A195456 A195457 * A195459 A195460 A195461

Keyword

nonn

Author

Peter Luschny, Sep 18 2011

Extensions

Better name from David Callan, Aug 14 2013

Status

approved