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Search: id:A119786
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| A119786 |
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Numerator of the product of the n-th triangular number and the n-th harmonic number. |
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+0
1
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| 1, 9, 11, 125, 137, 1029, 363, 6849, 7129, 81191, 83711, 1118273, 1145993, 1171733, 1195757, 41421503, 42142223, 813635157, 275295799, 279175675, 56574159, 439143531, 1332950097, 33695573875, 34052522467, 309561680403, 312536252003
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also numerator of the sum of all matrix elements of n X n matrix M[i,j] = i/j, i,j=1..n.
p^3 divides a(p-1) for prime p>3, p^3 divides a(p^2-1) 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[Sum[i,{i, 1, n}] * Sum[1/j,{j, 1, n}]] = numerator[n(n+1)/2 * Sum[1/i,{i, 1, n}]] = numerator[A000217(n) * (A001008(n)/A002805(n))]. Also a(n) = numerator[Sum[Sum[i/j,{i, 1, n}],{j, 1, n}]].
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MAPLE
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ZL:=n->sum(sum(j/i, i=1..n), j=1..n): a:=n->floor(numer(ZL(n))): seq(a(n), n=1..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 14 2007
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MATHEMATICA
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Numerator[Table[n(n+1)/2*Sum[1/i, {i, 1, n}], {n, 1, 50}]]. Numerator[Table[Sum[Sum[i/j, {i, 1, n}], {j, 1, n}], {n, 1, 50}]].
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CROSSREFS
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Cf. A000217, A001008, A002805.
Adjacent sequences: A119783 A119784 A119785 this_sequence A119787 A119788 A119789
Sequence in context: A058304 A027727 A019328 this_sequence A124606 A110647 A032687
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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), Jun 25 2006, Jul 12 2006
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EXTENSIONS
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Edited by njas at the suggestion of Andrew Plewe, May 27 2007
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