A136742 Product of the n-th run of squarefree numbers.

6, 210, 110, 2730, 17, 19, 10626, 26, 26970, 39270, 54834, 74046, 2162, 51, 53, 55, 195054, 3782, 287430, 342930, 5402, 474474, 6806, 635970, 89, 91, 830490, 97, 1061106, 1190910, 1330890, 1481430, 14042, 15006, 127, 2196870, 17822, 2627934

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2008

Keywords

• nonn

Comments

All terms are squarefree;

a(n) mod A072284(n) = 0;

A136743(n) = A001221(a(n)).

Examples

			n=10: A072284(10)=33, A120992(10)=3: a(10)=33*34*35=39270.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Squarefree

Crossrefs

Cf. A005117.

Programs

Maple

R:= NULL:
state:= false:
count:= 0:
for n from 1 while count < 100 do
if numtheory:-issqrfree(n) then
     if state then P:= P*n
     else P:= n; state:= true
     fi
  elif state then
     R:= R, P;
     count:= count+1;
     state:= false
  fi
od:
R; # Robert Israel, Jan 06 2020

Mathematica

Times @@ # & /@ DeleteCases[#, ?(! SquareFreeQ@ First@ # &)] &@ SplitBy[Range[140], SquareFreeQ] (* _Michael De Vlieger, Jan 06 2020 *)

Formula

a(n) = Product_{k=0..A120992(n)-1} (A072284(n)+k).