A180241 Numbers whose square can be expressed as the sum of a square, a cube and a fourth power, all positive.

5, 7, 8, 9, 12, 17, 18, 19, 21, 22, 23, 24, 25, 28, 31, 32, 33, 35, 37, 38, 39, 41, 42, 44, 45, 46, 47, 51, 52, 53, 54, 55, 57, 59, 60, 61, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 93, 95, 96, 97, 98, 99, 100, 101

Offset: 1

Author

Carmine Suriano, Aug 19 2010

Keywords

• nonn

Comments

a(n)^2 = x^2 + y^3 + z^4 with x,y,z > 0.

Examples

			a(5) = 12 is a term since 12*12 = 144 = 6^2 + 3^3 + 3^4 = 36 + 27 + 81.
		

Crossrefs

Cf. A180242, A256091, A256613, A255830.

Programs

PARI

for(D=1,99,for(C=1,sqrtn(D^2-1,4),for(B=1,sqrtn(D^2-C^4-1,3),issquare(D^2-C^4-B^3,&A)&&print1([A,B,C,D][4]",")+next(3)))) \\ M. F. Hasler, Apr 06 2015