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Search: id:A120284
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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
1
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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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COMMENT
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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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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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Cf. A061002, A001008.
Sequence in context: A001189 A101786 A012771 this_sequence A074440 A006204 A013572
Adjacent sequences: A120281 A120282 A120283 this_sequence A120285 A120286 A120287
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 07 2006
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