A120284 - OEIS

%I #6 Sep 14 2024 02:23:27

%S 3,9,25,125,147,343,761,6849,7381,81191,86021,1118273,1171733,1171733,

%T 2436559,41421503,42822903,271211719,279175675,55835135,19093197,

%U 439143531,1347822955,33695573875,34395742267,309561680403,315404588903

%N Numerator of absolute value of Sum_{k=1..n} (-1)^(k+1)*(2*k+1)*(Sum_{i=1..k} 1/i).

%C p^3 divides a(p-1) for prime p>3, a(p-1)/p^3=A061002[n], a(p-1)/p=A001008(p-1) for p>2. p^2 divides a(p-2) for prime p>3. p^3 divides a(p^2-1) for prime p>3. p divides a(p^2-2) for prime p>3. p^3 divides a(p^3-1) for prime p>3. p^3 divides a(p^4-1) for prime p>3.

%F a(n) = numerator(abs(Sum_{k=1..n} (-1)^(k+1)*(2*k+1)*(Sum_{i=1..k} 1/i))).

%t Numerator[Abs[Table[Sum[(-1)^(k+1)*(2k+1)*Sum[1/i,{i,1,k}],{k,1,n}],{n,1,30}]]]

%Y Cf. A061002, A001008.

%K frac,nonn

%O 1,1

%A _Alexander Adamchuk_, Jul 07 2006