A075987 Numerator(1+1/prime(1)^3+ ... + 1/prime(n)^3) where prime(k) is the k-th prime.

1, 9, 251, 31591, 10862713, 14467532003, 31797494201591, 156248170093443583, 1071839248022015186797, 13041980716182955257968099, 318091971114753602661286869511, 9476548712979446302049526230869201

Offset

0,2

Comments

The sum in the sequence has limit 1.1747626393. The case of reciprocal squares is in A075986.

For n>0 a(n) is the determinant of the n X n matrix with elements M[i,j] = 1+prime(i)^3 if i=j and 1 otherwise. - Alexander Adamchuk, Jul 08 2006

Links

Table of n, a(n) for n=0..11.

Simon Plouffe, Plouffe's Inverter

Formula

a(0) = 1; a(n) = a(n-1)*prime(n)^3+(prime(1)*...*prime(n-1))^3.

Example

a(2) = 251 so a(3) = 251*p(3)^3 + (2*3)^3 = 251*125 + 216 = 31591.

Mathematica

Table[Det[DiagonalMatrix[Table[Prime[i]^3, {i, 1, n}]]+1], {n, 1, 15}] (* Alexander Adamchuk, Jul 08 2006 *)

Prog

(PARI) a(n) = numerator(1 + sum(k=1, n, 1/prime(k)^3)); \\ Michel Marcus, May 31 2022

Crossrefs

Cf. A061015, A075986.

Sequence in context: A066989 A249593 A160501 * A135099 A073427 A303050

Adjacent sequences: A075984 A075985 A075986 * A075988 A075989 A075990

Keyword

nonn

Author

Zak Seidov, Sep 28 2002

Status

approved