A064646 Numerators of partial sums of reciprocals of primorial numbers.

1, 2, 7, 74, 543, 10589, 120009, 3420257, 4767631, 2281311434, 141441308909, 51307141467, 3301022547923, 200573000466191, 433638827007904943, 328326540448842314, 31534618884970203647, 13785884222546140694347

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

Limit_{n->oo} a(n)/A064647(n) = A064648. - Amiram Eldar, Feb 08 2025

Example

For n = 5, Sum_{j=1..5} 1/A002110(j) = 1/2 + 1/6 + 1/30 + 1/210 + 1/2310 = (1155 + 385 + 77 + 11 + 1)/2310 = 1629/2310 = 543/770, so a(5) = 543.

Mathematica

q[x_] := Apply[Times, Table[Prime[j], {j, 1, x}]]; a[n_] := Numerator[Apply[Plus, Table[1/q[w], {w, 1, n}]]]; Array[a, 18]

Prog

(PARI) list(lim) = {my(s = 0, pr = 1); forprime(p = 1, lim, pr *= p; s += 1/pr; print1(numerator(s), ", ")); } \\ Amiram Eldar, Feb 08 2025

Crossrefs

Cf. A002110, A064647 (denominators), A064648.

Sequence in context: A119811 A319621 A167526 * A366407 A144905 A349500

Adjacent sequences: A064643 A064644 A064645 * A064647 A064648 A064649

Keyword

frac,nonn

Author

Labos Elemer, Oct 04 2001

Status

approved