A054402 Numbers that are the sum of a positive square and a positive cube in more than one way.

17, 65, 89, 108, 129, 145, 225, 233, 252, 297, 316, 388, 449, 464, 505, 537, 548, 577, 593, 633, 730, 737, 745, 792, 793, 801, 873, 1025, 1088, 1090, 1116, 1289, 1304, 1305, 1367, 1412, 1441, 1452, 1529, 1585, 1601

Offset: 1

Author

Henry Bottomley, May 12 2000

Keywords

• easy
• nonn

Examples

			a(1)=17 since 17 = 3^2 + 2^3 = 4^2 + 1^3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055393, A055394.

Programs

Mathematica

lst={};Do[Do[AppendTo[lst,n^2+m^3],{n,5!}],{m,5!}];lst=Sort[lst]; lst2={};Do[If[lst[[n]]==lst[[n+1]],AppendTo[lst2,lst[[n]]]],{n,Length[lst]-1}];lst2; Take[Union[lst2],123] (* Vladimir Joseph Stephan Orlovsky, Jul 17 2009 *)

PARI

list(lim)=my(v=List(),u=List());for(n=1,sqrtint(lim\1-1), for(m=1, sqrtnint(lim\1-n^2,3), listput(v,n^2+m^3))); v=vecsort(v); for(i=2,#v, if(v[i]==v[i-1], listput(u,v[i]))); Set(u) \\ Charles R Greathouse IV, May 15 2015