A115964 Denominator of Sum_{i=1..n} 1/prime(i)^3.

8, 216, 27000, 9261000, 12326391000, 27081081027000, 133049351085651000, 912585499096480209000, 11103427767506874702903000, 270801499821725167129101267000, 8067447481189014453943055845197000

Offset: 1

Author

Jonathan Vos Post, Mar 14 2006

Keywords

• easy
• frac
• nonn

Comments

Numerators are in A115963.

Also the primorials cubed. - Reikku Kulon, Sep 18 2008

Examples

			1/8, 35/216, 4591/27000, 1601713/9261000, 2141141003/12326391000, 4716413174591/27081081027000.
		

Crossrefs

Cf. A115963 (numerators).

Cf. A024451 (numerator of sum_{i=1..n} 1/prime(i)), A002110 (primorial, also denominator of sum_{i=1..n} 1/prime(i)), A061015 (numerator of sum_{i=1..n} 1/prime(i)^2).

Cf. A000040, A075986/A075987, A106830/A034386.

Cf. A061742, A100778. - Reikku Kulon, Sep 18 2008

Programs

Mathematica

a[n_]:=Product[Prime[i]^3, {i, 1, n}]; (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *)

Formula

a(n) = denominator of Sum_{i=1..n} 1/A000040(i)^3.

a(n) = A002110(n)^3. - Reikku Kulon, Sep 18 2008