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A082875 Squares that are the sum of three factorials. 3
4, 9, 36, 49, 841, 5184 (list; graph; refs; listen; history; text; internal format)
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: A272221 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

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Last modified October 17 01:59 EDT 2019. Contains 328105 sequences. (Running on oeis4.)