A064647 Denominators of partial sums of reciprocals of primorial numbers.

2, 3, 10, 105, 770, 15015, 170170, 4849845, 6760390, 3234846615, 200560490130, 72752334655, 4680773285034, 284407855036305, 614889782588491410, 465559406817000639, 44715356980330526490, 19548063559901161830545

Offset

1,1

Links

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

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) = 770.

Mathematica

q[x_] := Apply[Times, Table[Prime[j], {j, 1, x}]]; a[n_] := Denominator[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(denominator(s), ", ")); } \\ Amiram Eldar, Feb 08 2025

Crossrefs

Cf. A002110, A064646 (numerators).

Sequence in context: A229220 A155148 A076927 * A119810 A055708 A162647

Adjacent sequences: A064644 A064645 A064646 * A064648 A064649 A064650

Keyword

frac,nonn

Author

Labos Elemer, Oct 04 2001

Status

approved