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

1,3

Comments

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

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

Links

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

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

Example

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

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 *)

Prog

(Magma) [(HarmonicNumber(n)-1)*Lcm([1..n]): n in [1..30]]; // Vincenzo Librandi, Dec 14 2016
(PARI) a(n) = (sum(i=1, n, 1/i)-1)*lcm([1..n]); \\ Michel Marcus, Jul 23 2022

Crossrefs

Cf. A001008, A002805, A003418.

Sequence in context: A294208 A081525 A027612 * A113876 A333082 A214536

Adjacent sequences: A027454 A027455 A027456 * A027458 A027459 A027460

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved