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A027457 a(n) = (H(n) - 1)*lcm{1,...,n}, where H(n) is the n-th harmonic number. 3
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 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Cf. A001008, A002805, A003418.

Sequence in context: A294208 A081525 A027612 * A113876 A214536 A324418

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

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Last modified May 26 23:51 EDT 2019. Contains 323597 sequences. (Running on oeis4.)