The On-Line Encyclopedia of Integer Sequences (OEIS)

A115964 revision #4

A115964

Denominator of Sum[i=1..n] 1/p(i)^3, p(i) = i-th prime.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Numerators = A115963. See also: A024451 Numerator of Sum 1/prime(i), i=1..n. A002110 Primorial [denominator of Numerator of Sum 1/prime(i), i=1..n]. A061015 Numerator of Sum_{i=1..n} 1/p(i)^2, p(i) = i-th prime.

Also the primorials cubed. [From Reikku Kulon, Sep 18 2008]

LINKS

Table of n, a(n) for n=1..11.

FORMULA

a(n) = Denominator of Sum[i=1..n] 1/A000040(i)^3.

a(n) = A002110(n)^3 [From Reikku Kulon, Sep 18 2008]

EXAMPLE

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

MATHEMATICA

a[n_]:=Product[Prime[i]^3, {i, 1, n}]; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 05 2008]

CROSSREFS

Cf. A000040, A075986/A075987, A106830/A034386, A115963.