

A140823


Natural numbers which are not perfect fourth powers.


1



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
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OFFSET

1,1


COMMENTS

First differs from A046100 at {32, 48, 64, 80, 96, 112, 144, 160, 162, ...}.
What formula does dos Reis provide analogous to the formulas 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*(n1)/2)  A000538(j < n^(1/4)) = (n*(n1)/2)  (j*(1+j)*(1+2*j)*(1+3*j+3*j^2)/30) for j < [n^(1/4)].


LINKS

Table of n, a(n) for n=1..72.
A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, Math. Mag., 63 (1990), 5355.


FORMULA

{a(n) in A000027 and a(n) not in A000583} = (n in A000027 and a(n) <> k^4}.


MATHEMATICA

Module[{nn=100, fp}, fp=Floor[Surd[nn, 4]]; Complement[Range[nn], Range[ fp]^4]] (* Harvey P. Dale, Dec 09 2013 *)


CROSSREFS

Cf. A000037, A000583, A007412, A046100.
Sequence in context: A032951 A288139 A194897 * A209061 A115063 A178210
Adjacent sequences: A140820 A140821 A140822 * A140824 A140825 A140826


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jul 17 2008


STATUS

approved



