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A099827
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Generalized harmonic number H(n,5) multiplied by (n!)^5. H(n,5) = Sum{1/k^5), k = 1..n. H(n,5) = 1, 33/32, 8051/7776, 257875/248832,... (A099828 - numerator).
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3
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1, 33, 8051, 8252000, 25795462624, 200610400564224, 3371852494046112768, 110492114540967125581824, 6524555433591956305924325376, 652461835742417609568446054400000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Note a(n) is divisible by n, except when n is prime. a(n+1) is divisible by n, except when n is prime.
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LINKS
| Eric Weisstein's World of Mathematics, Harmonic Number
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FORMULA
| a(n) = (n!)^5 * Sum[1/k^5, {k, 1, n}] a(n) = (n!)^5 * HarmonicNumber[n, 5]
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EXAMPLE
| a(2) = (2!)^5 * (1 + 1/2^5) = 2^5 + 1 = 33,
a(3) = (3!)^5 * (1 + 1/2^5 + 1/3^5) = 6^5 + 3^5 + 1 = 8051.
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MATHEMATICA
| Table[(n!)^5*Sum[1/k^5, {k, 1, n}], {n, 1, 13}] or Table[(n!)^5*HarmonicNumber[n, 5], {n, 1, 13}]
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CROSSREFS
| Cf. A099828 A001008.
Sequence in context: A057981 A183237 A099828 * A060705 A061687 A116056
Adjacent sequences: A099824 A099825 A099826 * A099828 A099829 A099830
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2004
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