A064858 Denominators of partial sums of reciprocals of lcm(1..n) = A003418(n).

1, 2, 3, 4, 30, 60, 14, 840, 315, 504, 6930, 9240, 180180, 360360, 30030, 720720, 2042040, 2450448, 10581480, 1989680, 58198140, 232792560, 1338557220, 254963280, 13385572200, 26771144400, 5736673800, 6177956400, 291136195350

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) = 14.
		

Links

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

Crossrefs

Cf. A003418, A064857, 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(denom, P); # Robert Israel, Jan 30 2025

Mathematica

q[x_] := Apply[LCM, Table[j, {j, 1, x}]] Table[Denominator[Apply[Plus, Table[1/q[w], {w, 1, m}]]], {m, 1, 30}]

Formula

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