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%I #2 Mar 31 2012 13:20:27
%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[(-1)^(k+1)*(2k+1)*Sum[1/i,{i,1,k}],{k,1,n}]]].
%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[(-1)^(k+1)*(2k+1)*Sum[1/i,{i,1,k}],{k,1,n}]]].
%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
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