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A082875
Squares that are the sum of three factorials.
3
4, 9, 36, 49, 841, 5184
OFFSET
1,1
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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, May 25 2003
EXTENSIONS
Sequence data ordered by Michel Marcus, Jun 03 2013
STATUS
approved