A140823 Integers that are not perfect fourth powers.

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

Offset: 1

Author

Jonathan Vos Post, Jul 17 2008

Keywords

• easy
• nonn

Comments

First differs from A046100 at {32, 48, 64, 80, 96, 112, 144, 160, 162, ...}.

Links

• A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, Math. Mag., 63 (1990), 53-55.

Crossrefs

Cf. A000037, A000583, A007412, A046100.

Programs

Mathematica

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

Python

from sympy import integer_nthroot
def A140823(n): return n+(k:=integer_nthroot(n,4)[0])+int(n>=(k+1)**4-k) # Chai Wah Wu, Jun 17 2024

Formula

{a(n) in A000027 and a(n) not in A000583}.