A125110 Cubes which have a partition as the sum of 2 squares.

0, 1, 8, 64, 125, 512, 729, 1000, 2197, 4096, 4913, 5832, 8000, 15625, 17576, 24389, 32768, 39304, 46656, 50653, 64000, 68921, 91125, 117649, 125000, 140608, 148877, 195112, 226981, 262144, 274625, 314432, 373248, 389017, 405224, 512000, 531441

Offset: 1

Author

Artur Jasinski, Nov 21 2006

Keywords

• nonn

Examples

			125 = 5^3 = 2^2 + 11^2 = A001481(54) = A000578(8).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125084, A125111, A001481.

Programs

Mathematica

Select[Range[0, 81]^3, SquaresR[2, # ] > 0 &] (* Ray Chandler, Nov 23 2006 *)

PARI

isA125110(ncube)={ local(a) ; a=0; while(a^2<=ncube, if(issquare(ncube-a^2), return(1) ; ) ; a++ ; ) ; return(0) ; } { for(n=0,200, if(isA125110(n^3), print1(n^3,",") ; ) ; ) ; } \\ R. J. Mathar, Nov 23 2006

Python

from itertools import count, islice
from sympy import factorint
def A125110_gen(): # generator of terms
    return map(lambda m:m**3,filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n).items()),count(0)))
A125110_list = list(islice(A125110_gen(),20)) # Chai Wah Wu, Jun 27 2022

Formula

a(n) = A001481(n)^3. - Ray Chandler, Nov 23 2006

Equals A000578 INTERSECT A001481. - R. J. Mathar, Nov 23 2006

Extensions

Corrected and extended by R. J. Mathar and Ray Chandler, Nov 23 2006