A027457 a(n) = (H(n) - 1)*lcm{1,...,n}, where H(n) is the n-th harmonic number.

0, 1, 5, 13, 77, 87, 669, 1443, 4609, 4861, 55991, 58301, 785633, 811373, 835397, 1715839, 29889983, 30570663, 593094837, 604734465, 615819825, 626401305, 14640022575, 14863115445, 75386423001, 76416082401, 232222818803, 235091155703, 6897956948587

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Comments

Second column of A027446. - Olivier Gérard, Dec 11 1999

Rows sums of (A002262*A096180). - Eric Desbiaux, Apr 23 2013

Examples

			a(3) = (1/2+1/3)*lcm(2,3) = 5.
		

Links

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

Crossrefs

Cf. A001008, A002805, A003418.

Programs

Magma

[(HarmonicNumber(n)-1)*Lcm([1..n]): n in [1..30]]; // Vincenzo Librandi, Dec 14 2016

Maple

A027457 := n -> (Psi(n+1)-1+gamma)*lcm(seq(k,k=1..n)): # Peter Luschny, Dec 01 2011
# alternative:
A[1]:= 0: L[1]:= 1:
for n from 1 to 50 do
   L[n+1]:= ilcm(L[n],n+1);
   A[n+1]:= L[n+1]*(A[n]/L[n] + 1/(n+1))
od:
seq(A[n],n=1..50); # Robert Israel, Dec 14 2016

Mathematica

a[n_] := (HarmonicNumber[n] - 1)*LCM @@ Range[n]; Table[a[n], {n, 1, 29}] (* Jean-François Alcover, Mar 05 2013 *)

PARI

a(n) = (sum(i=1, n, 1/i)-1)*lcm([1..n]); \\ Michel Marcus, Jul 23 2022

Formula

Numerators of sequence a[ 2, n ] in (a[ i, j ])^2 where a[ i, j ] = 1/i if j<=i, 0 if j>i. - N. J. A. Sloane, Feb 24 2006

a(n) = (Psi(n+1)-1+gamma)*LCM(n), LCM(n) = lcm{1..n}. - Peter Luschny, Dec 01 2011

a(n+1) = A003418(n+1)*(a(n)/A003418(n)+1/(n+1)). - Robert Israel, Dec 14 2016

Extensions

New name, offset changed to 1, a(1) and a(21)-a(29) added. - Peter Luschny, Dec 01 2011