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A128670
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Least number k > 0 such that k^n does not divide the denominator of generalized harmonic number H(k,n) nor the denominator of alternating generalized harmonic number H'(k,n).
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4
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77, 20, 94556602, 42, 444, 20, 104, 42, 76, 20, 77, 110, 3504, 20, 903, 42, 1107, 20, 104, 42, 77, 20, 2948, 110, 136, 20, 76, 42, 903, 20, 77, 42, 268, 20, 7004, 110, 1752, 20, 19203, 42, 77, 20, 104, 42, 76, 20, 370, 110, 1107, 20, 77, 42, 12246, 20, 104, 42
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OFFSET
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1,1
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COMMENTS
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Generalized harmonic numbers are defined as H(m,k) = Sum_{j=1..m}1/j^k. Alternating generalized harmonic numbers are defined as H'(m,k) = Sum_{j=1..m} (-1)^(j+1)/j^k.
Some apparent periodicity in {a(n)} (not without exceptions): a(n) = 20 for n = 2 + 4m, a(n) = 42 for n = 4 + 12m and 8 + 12m, a(n) = 76 for n = 9 + 18m, a(n) = 77 for n = 1 + 10m, a(n) = 104 for n = 7 + 12m, a(n) = 110 for n = 12m, a(n) = 136 for n = 25 + 32m, etc.
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LINKS
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CROSSREFS
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Cf. A001008, A002805, A058313, A058312, A007406, A007407, A119682, A007410, A120296, A125581, A126196, A126197, A128672, A128673, A128674, A128675, A128676, A128671, A128670.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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