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

%I A125110 #27 Apr 28 2025 11:54:09
%S A125110 0,1,8,64,125,512,729,1000,2197,4096,4913,5832,8000,15625,17576,24389,
%T A125110 32768,39304,46656,50653,64000,68921,91125,117649,125000,140608,
%U A125110 148877,195112,226981,262144,274625,314432,373248,389017,405224,512000,531441
%N A125110 Cubes which have a partition as the sum of 2 squares.
%H A125110 Amiram Eldar, <a href="/A125110/b125110.txt">Table of n, a(n) for n = 1..10000</a>
%F A125110 a(n) = A001481(n)^3. - _Ray Chandler_, Nov 23 2006
%F A125110 Equals A000578 INTERSECT A001481. - _R. J. Mathar_, Nov 23 2006
%e A125110 125 = 5^3 = 2^2 + 11^2 = A001481(54) = A000578(8).
%t A125110 Select[Range[0, 81]^3, SquaresR[2, # ] > 0 &] (* _Ray Chandler_, Nov 23 2006 *)
%o A125110 (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
%o A125110 (Python)
%o A125110 from itertools import count, islice
%o A125110 from sympy import factorint
%o A125110 def A125110_gen(): # generator of terms
%o A125110     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)))
%o A125110 A125110_list = list(islice(A125110_gen(),20)) # _Chai Wah Wu_, Jun 27 2022
%Y A125110 Cf. A125084, A125111, A001481.
%K A125110 nonn
%O A125110 1,3
%A A125110 _Artur Jasinski_, Nov 21 2006
%E A125110 Corrected and extended by _R. J. Mathar_ and _Ray Chandler_, Nov 23 2006