A125900 - OEIS

A125900

Triangle of the numerators of the almost-harmonic numbers: n-th term in m-th row is numerator of (sum{k=1 to m} 1/k) - 1/n, 1<=n<=m.

%I #11 Oct 10 2019 14:04:07

%S 0,1,1,5,4,3,13,19,7,11,77,107,39,61,25,29,39,127,11,9,137,223,293,

%T 949,82,67,1019,49,481,621,2003,691,141,2143,103,363,4609,5869,6289,

%U 6499,1325,6709,967,3407,761,4861,6121,6541,6751,6877,6961,1003,3533,789

%N Triangle of the numerators of the almost-harmonic numbers: n-th term in m-th row is numerator of (sum{k=1 to m} 1/k) - 1/n, 1<=n<=m.

%e Triangle of almost-harmonic numbers begins:

%e 0

%e 1/2,1

%e 5/6,4/3,3/2

%e 13/12,19/12,7/4,11/6

%e 77/60,107/60,39/20,61/30,25/12

%t t[m_, n_] := Sum[1/k, {k, m}] - 1/n;Numerator @ Flatten @ Table[t[m, n], {m, 10}, {n, m}] (* _Ray Chandler_, Dec 14 2006 *)

%Y Cf. A125901.

%K frac,nonn,tabl

%O 1,4

%A _Leroy Quet_, Dec 13 2006

%E Extended by _Ray Chandler_, Dec 14 2006