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A120284
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Numerator of absolute value of Sum[(-1)^(k+1)*(2k+1)*Sum[1/i,{i,1,k}],{k,1,n}]]].
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0
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3, 9, 25, 125, 147, 343, 761, 6849, 7381, 81191, 86021, 1118273, 1171733, 1171733, 2436559, 41421503, 42822903, 271211719, 279175675, 55835135, 19093197, 439143531, 1347822955, 33695573875, 34395742267, 309561680403, 315404588903
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = numerator[Abs[Sum[(-1)^(k+1)*(2k+1)*Sum[1/i,{i,1,k}],{k,1,n}]]].
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MATHEMATICA
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Numerator[Abs[Table[Sum[(-1)^(k+1)*(2k+1)*Sum[1/i, {i, 1, k}], {k, 1, n}], {n, 1, 30}]]]
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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