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Sum of a positive square and a positive cube in at least three ways.
1

%I #6 May 14 2019 22:02:05

%S 1025,1737,2089,2628,2817,3033,3664,4481,4825,4977,5841,7057,7785,

%T 7948,8225,8289,8900,10025,11025,11665,12393,14049,14400,14724,15193,

%U 15345,15641,15689,15884,16649,16857,18201,18369,19225,19664,19908,20224

%N Sum of a positive square and a positive cube in at least three ways.

%C Four or more representations have 1025, 19225, 27289, 29025, 39329, 48025, 54225, 65537, 65600, 79129, 92025, 93241, 105192, 105633, 111681, ... - _R. J. Mathar_, Dec 11 2009

%e 1025 = 32^2 + 1^3, 31^2 + 4^3, 30^2 + 5^3, and 5^2 + 10^3;

%e 1737 = 35^2 + 8^3, 3^2 + 12^3, and 39^2 + 6^3.

%p isA171385 := proc(n) a := 0 ; for c from 1 do if c^3 >= n then break; else if issqr(n-c^3) then a := a+1 ; end if; end if; end do ; a >= 3 ; end proc: for n from 2 to 120000 do if isA171385(n) then printf("%d,",n) ; fi; end do ; # _R. J. Mathar_, Dec 11 2009

%Y Cf. A054402, integers with two or more such representations.

%K easy,nonn

%O 1,1

%A _Alan Frank_, Dec 07 2009

%E More terms from _R. J. Mathar_, Dec 11 2009