A115963 Numerator of Sum_{i=1..n} 1/prime(i)^3.

1, 35, 4591, 1601713, 2141141003, 4716413174591, 23198819007792583, 159253748925534977797, 1938552948676080555065099, 47290471293028435532185602511, 1409101231790431848106470385672201

Offset: 1

Author

Jonathan Vos Post, Mar 14 2006

Keywords

• easy
• frac
• nonn

Comments

Denominators = A115964. See also: A024451 Numerator of Sum_{i=1..n} 1/prime(i). A002110 Primorial [denominator of Numerator of Sum_{i=1..n} 1/prime(i)]. A061015 Numerator of Sum_{i=1..n} 1/prime(i)^2.

Examples

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

Crossrefs

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

Programs

Mathematica

Accumulate[1/Prime[Range[20]]^3]//Numerator (* Harvey P. Dale, Dec 30 2024 *)

Formula

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