A064646 - OEIS

%I #11 Feb 08 2025 04:51:57

%S 1,2,7,74,543,10589,120009,3420257,4767631,2281311434,141441308909,

%T 51307141467,3301022547923,200573000466191,433638827007904943,

%U 328326540448842314,31534618884970203647,13785884222546140694347

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

%F Limit_{n->oo} a(n)/A064647(n) = A064648. - _Amiram Eldar_, Feb 08 2025

%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) = 543.

%t 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]

%o (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

%Y Cf. A002110, A064647 (denominators), A064648.

%K frac,nonn

%O 1,2

%A _Labos Elemer_, Oct 04 2001