A140823 -id:A140823 - cp's OEIS frontend

A373868 Integers that are not perfect fifth powers.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 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

Offset: 1

Chai Wah Wu, Jun 19 2024

Complement of A000584.

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

Cf. A000037, A000583, A000584, A007412, A140823.

Complement[Range[#^5], Range[#]^5] & [3] (* Paolo Xausa, Jul 03 2024 *)

from sympy import integer_nthroot
def A373868(n): return n+(k:=integer_nthroot(n, 5)[0])+(n>=(k+1)**5-k)

A305553 Numbers that are not the sum of 2 squares and a 4th power.

Original entry on oeis.org

7, 12, 15, 22, 23, 28, 31, 39, 43, 44, 47, 55, 60, 63, 67, 70, 71, 76, 78, 79, 87, 92, 93, 95, 103, 108, 111, 112, 119, 124, 127, 135, 140, 143, 151, 156, 159, 167, 168, 172, 175, 177, 183, 184, 188, 191, 192, 199, 204, 207, 214, 215, 220, 223, 231, 236

Offset: 1

XU Pingya, Jun 20 2018

nonn

Numbers of the form 4*A017101(k) are terms of this sequence.

m is a term iff 16m is also.

W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169-173.

Subsequence of A000037, A140823 and A022544.
A004215 and A214891 are subsequences.
Cf. A017101, A022552.

n=239;
t=Union@Flatten@Table[x^2+y^2+z^4, {x,0,n^(1/2)}, {y,x,(n-x^2)^(1/2)}, {z,0,(n-x^2-y^2)^(1/4)}];
Complement[Range[0,n], t]

cp's OEIS Frontend

A373868 Integers that are not perfect fifth powers.

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