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Search: id:A140823
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| A140823 |
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Natural numbers which are not perfect fourth powers. |
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+0
1
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| 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First differs from A046100 at {32, 48, 64, 80, 96, 112, 144, 160, 162, ...}. What formula does dos Reis provide analogous to the formulae for nonsquares A000037(n) = n + [1/2 + sqrt(n)] and noncubes A007412(n) = n + [(n + [n^{1/3}])^{1/3}]? The partial sum of nonbiquadratic numbers < n is (the sum of all natural numbers < n) - (the sum of 4th powers k^4 < n) = (n*(n-1)/2) - A000538(j < n^(1/4)) = (n*(n-1)/2) - (j*(1+j)*(1+2*j)*(-1+3*j+3*j^2)/30) for j < [n^(1/4)].
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REFERENCES
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A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, Math. Mag., 63 (1990), 53-55.
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FORMULA
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{a(n) in A000027 and a(n) not in A000583} = (n in A000027 and a(n) <> k^4}.
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CROSSREFS
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Cf. A000037, A000583, A007412, A046100.
Sequence in context: A023770 A023797 A032951 this_sequence A115063 A013938 A023809
Adjacent sequences: A140820 A140821 A140822 this_sequence A140824 A140825 A140826
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 17 2008
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