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

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) = 543.
		

Crossrefs

Cf. A002110, A064647 (denominators), A064648.

Programs

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]

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

Formula

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