A127600 Integer part of cube root of product of first n primes.

1, 1, 3, 5, 13, 31, 79, 213, 606, 1863, 5853, 19505, 67257, 235631, 850352, 3194167, 12434883, 48949883, 198812307, 823245530, 3440622312, 14763161313, 64397952985, 287520444756, 1321070444052, 6152237618431, 28838910052201

Offset: 1

Author

Artur Jasinski, Jan 19 2007

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..898

Crossrefs

Cf. A002110, A060797.

Programs

Maple

Res:= NULL:
p:= 1: r:= 1:
for n from 1 to 50 do
  p:=nextprime(p);
  r:= r*p;
  Res:= Res, floor(r^(1/3));
od:
Res; # Robert Israel, Nov 10 2017

Mathematica

a = {}; Do[b = 1; Do[b = b Prime[x], {x, 1, n}]; AppendTo[a, Floor[b^(1/3)]], {n, 1, 100}]; a (* Artur Jasinski *)
Floor[Surd[#,3]]&/@Rest[FoldList[Times,1,Prime[Range[30]]]] (* Harvey P. Dale, Jun 23 2014 *)

PARI

a(n) = sqrtnint(prod(k=1, n, prime(k)), 3); \\ Michel Marcus, Nov 10 2017