A136742 - OEIS

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

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OFFSET

1,1

COMMENTS

All terms are squarefree;

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

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Squarefree

FORMULA

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

EXAMPLE

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

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

elif state then

R:= R, P;

count:= count+1;

state:= false

od:

R; # Robert Israel, Jan 06 2020

MATHEMATICA

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

CROSSREFS

Cf. A005117.

Sequence in context: A172530 A201237 A120436 * A334285 A068969 A335715

Adjacent sequences: A136739 A136740 A136741 * A136743 A136744 A136745

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 20 2008

STATUS

approved