A064857 Numerators of partial sums of reciprocals of lcm(1..n) = A003418(n).

1, 3, 5, 7, 53, 107, 25, 1501, 563, 901, 12389, 16519, 322121, 644243, 53687, 1288489, 3650719, 4380863, 18917363, 3557111, 104045497, 416181989, 2393046437, 455818369, 23930464373, 47860928747, 10255913303, 11044829711

Offset: 1

Author

Labos Elemer, Oct 08 2001

Keywords

• nonn
• frac

Examples

			n = 7: LCM values: 1, 2, 6, 12, 60, 60, 420; partial sum = 1 + 1/2 + 1/6 + 1/12 + 1/60 + 1/60 + 1/420 = (420 + 210 + 70 + 35 + 7 + 7 + 1)/420 = 750/420 = 25/14, so a(7) = 25.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2296

Crossrefs

Cf. A003418, A064858, A064859.

Programs

Maple

R:= 1: m:= 1: for n from 2 to 100 do m:= ilcm(m,n); R:= R,1/m od:
P:= ListTools:-PartialSums([R]):
map(numer,P); # Robert Israel, Jan 30 2025

Mathematica

q[x_] := Apply[LCM, Table[j, {j, 1, x}]] Table[Numerator[Apply[Plus, Table[1/q[w], {w, 1, m}]]], {m, 1, 30}]
Accumulate[Table[1/LCM@@Range[n],{n,30}]]//Numerator (* Harvey P. Dale, Aug 08 2021 *)

Formula

a(n) = numerator(Sum_{j=1..n} 1/lcm(1..n)).