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

Author

Labos Elemer, Oct 04 2001

Keywords

• frac
• nonn

Examples

			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.
		

Crossrefs

Cf. A002110, A064646 (numerators).

Programs

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]

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