A109819 Product of primes between n and n^2.

1, 6, 105, 5005, 37182145, 6685349671, 20496326086283047, 558516101711461766587, 15322117939717490037614688353, 10978895066407230594062391177770267, 150524069716274322800691458531160297587022319, 4335344870389259769484516507207766258600144871515339

Offset: 1

Author

Rick L. Shepherd, Jul 02 2005

Keywords

• easy
• nonn

Examples

			a(3) = 105 because 3, 5 and 7 are the A073882(3) = 3 primes in the interval from 3 to 3^2 inclusive and 3 * 5 * 7 = 105.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A109818 (sum of same primes), A073882 (number of primes between n and n^2).

Programs

Mathematica

Join[{1},Table[Product[Prime[i],{i,If[PrimeQ[n],PrimePi[n],PrimePi[n]+1],PrimePi[n^2]}],{n,2,10}]] (* James C. McMahon, Apr 01 2024 *)

PARI

for(n=1,15,print1(prod(k=n,n^2,if(isprime(k),k,1)),","))

Formula

log(a(n)) ~ n^2 by the Prime Number Theorem. - Charles R Greathouse IV, Feb 05 2025

Extensions

More terms from Michel Marcus, Apr 02 2024