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

1,1

Comments

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

Links

Table of n, a(n) for n=1..70.

Example

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

Prog

(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

Crossrefs

Cf. A180242, A256091, A256613, A255830.

Sequence in context: A157724 A080644 A309277 * A047479 A080720 A189034

Adjacent sequences: A180238 A180239 A180240 * A180242 A180243 A180244

Keyword

nonn

Author

Carmine Suriano, Aug 19 2010

Status

approved