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

%I A027457 #34 Sep 08 2022 08:44:49
%S A027457 0,1,5,13,77,87,669,1443,4609,4861,55991,58301,785633,811373,835397,
%T A027457 1715839,29889983,30570663,593094837,604734465,615819825,626401305,
%U A027457 14640022575,14863115445,75386423001,76416082401,232222818803,235091155703,6897956948587
%N A027457 a(n) = (H(n) - 1)*lcm{1,...,n}, where H(n) is the n-th harmonic number.
%C A027457 Second column of A027446. - _Olivier Gérard_, Dec 11 1999
%C A027457 Rows sums of (A002262*A096180).  - _Eric Desbiaux_, Apr 23 2013
%H A027457 Robert Israel, <a href="/A027457/b027457.txt">Table of n, a(n) for n = 1..2296</a>
%F A027457 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
%F A027457 a(n) = (Psi(n+1)-1+gamma)*LCM(n), LCM(n) = lcm{1..n}. - _Peter Luschny_, Dec 01 2011
%F A027457 a(n+1) = A003418(n+1)*(a(n)/A003418(n)+1/(n+1)). - _Robert Israel_, Dec 14 2016
%e A027457 a(3) = (1/2+1/3)*lcm(2,3) = 5.
%p A027457 A027457 := n -> (Psi(n+1)-1+gamma)*lcm(seq(k,k=1..n)): # _Peter Luschny_, Dec 01 2011
%p A027457 # alternative:
%p A027457 A[1]:= 0: L[1]:= 1:
%p A027457 for n from 1 to 50 do
%p A027457    L[n+1]:= ilcm(L[n],n+1);
%p A027457    A[n+1]:= L[n+1]*(A[n]/L[n] + 1/(n+1))
%p A027457 od:
%p A027457 seq(A[n],n=1..50); # _Robert Israel_, Dec 14 2016
%t A027457 a[n_] := (HarmonicNumber[n] - 1)*LCM @@ Range[n]; Table[a[n], {n, 1, 29}] (* _Jean-François Alcover_, Mar 05 2013 *)
%o A027457 (Magma) [(HarmonicNumber(n)-1)*Lcm([1..n]): n in [1..30]]; // _Vincenzo Librandi_, Dec 14 2016
%o A027457 (PARI) a(n) = (sum(i=1, n, 1/i)-1)*lcm([1..n]); \\ _Michel Marcus_, Jul 23 2022
%Y A027457 Cf. A001008, A002805, A003418.
%K A027457 nonn
%O A027457 1,3
%A A027457 _Olivier Gérard_
%E A027457 New name, offset changed to 1, a(1) and a(21)-a(29) added. - _Peter Luschny_, Dec 01 2011