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A082875
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Squares that are the sum of three factorials.
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1
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OFFSET
| 0,1
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FORMULA
| a1! + a2! + a3! = z^2.
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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
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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}]
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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" ")) ) ) ) }
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CROSSREFS
| Sequence in context: A081069 A053967 A028945 * A086541 A053965 A058444
Adjacent sequences: A082872 A082873 A082874 * A082876 A082877 A082878
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), May 25 2003
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