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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 (list; graph; refs; listen; history; text; internal format)
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*(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)].

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), 53-55.

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

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Last modified November 28 04:31 EST 2021. Contains 349400 sequences. (Running on oeis4.)