A082875 Squares that are the sum of three factorials.

4, 9, 36, 49, 841, 5184

Offset

1,1

Links

Table of n, a(n) for n=1..6.

Formula

a1! + a2! + a3! = z^2.

Example

These appear to be the only solutions. 8 and 27 appear to be the only cubes that are the sum of 3 factorials. Again, it appears that 2 and 3 are the only powers of n satisfying a1!+a2!+a3! = z^n.
The complete list of solutions is
a1 a2 a3 z^2
0 0 2 4
0 1 2 4
0 2 3 9
0 4 4 49
0 5 6 841
1 1 2 4
1 2 3 9
1 4 4 49
1 5 6 841
3 3 4 36
4 5 7 5184

Mathematica

d = 50; a = Union[ Flatten[ Table[a! + b! + c!, {a, 1, d}, {b, a, d}, {c, b, d}]]]; l = Length[a]; Do[ If[ IntegerQ[ Sqrt[ a[[i]]]], Print[ a[[i]]]], {i, 1, l}]

Prog

(PARI) sum3factsq(n) = { for(a1=1, n, for(a2=a1, n, for(a3=a2, n, z = a1!+a2!+a3!; if(issquare(z), print1(z" ")) ) ) ) }

Crossrefs

Cf A114377, A162681.

Sequence in context: A334110 A117676 A085575 * A267430 A117756 A326182

Adjacent sequences: A082872 A082873 A082874 * A082876 A082877 A082878

Keyword

easy,nonn

Author

Cino Hilliard, May 25 2003

Extensions

Sequence data ordered by Michel Marcus, Jun 03 2013

Status

approved