A064647 - OEIS

%I #13 Feb 08 2025 04:52:02

%S 2,3,10,105,770,15015,170170,4849845,6760390,3234846615,200560490130,

%T 72752334655,4680773285034,284407855036305,614889782588491410,

%U 465559406817000639,44715356980330526490,19548063559901161830545

%N Denominators of partial sums of reciprocals of primorial numbers.

%e 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.

%t 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]

%o (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

%Y Cf. A002110, A064646 (numerators).

%K frac,nonn

%O 1,1

%A _Labos Elemer_, Oct 04 2001