A081971 - OEIS

A081971

Consider the harmonic progression 1,1/2,1/3,1/4,1/5,..., group the terms such that the n-th group contains n members like this (1/1),(1/2,1/3),(1/4,1/5,1/6), (1/7,1/8,1/9,1/10),... a(n) = the numerator of the reduced rational sum of the terms of the n-th group.

%I #5 Dec 05 2013 19:56:03

%S 1,5,37,1207,7793,532541,35036093,419218787,98431469723,

%T 14642854403167,6408932966879,4075936031956831,504163702484694137,

%U 78452289445098136367,9442422052170405158543,711841627568479091422201

%N Consider the harmonic progression 1,1/2,1/3,1/4,1/5,..., group the terms such that the n-th group contains n members like this (1/1),(1/2,1/3),(1/4,1/5,1/6), (1/7,1/8,1/9,1/10),... a(n) = the numerator of the reduced rational sum of the terms of the n-th group.

%C Equivalently, numerator of sum_{i=n(n-1)/2+1..n(n+1)/2} 1/i.

%o (PARI) nsn(n) = numerator(sum(i = n*(n-1)/2+1, n*(n+1)/2, 1/i)); \\ _Michel Marcus_, Aug 29 2013

%Y Denominator is in A082681.

%K nonn,frac

%O 1,2

%A _Amarnath Murthy_, Apr 03 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 08 2003