login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082875 Squares that are the sum of three factorials. 3

%I #9 Oct 01 2013 17:57:38

%S 4,9,36,49,841,5184

%N Squares that are the sum of three factorials.

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

%e 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.

%e The complete list of solutions is

%e a1 a2 a3 z^2

%e 0 0 2 4

%e 0 1 2 4

%e 0 2 3 9

%e 0 4 4 49

%e 0 5 6 841

%e 1 1 2 4

%e 1 2 3 9

%e 1 4 4 49

%e 1 5 6 841

%e 3 3 4 36

%e 4 5 7 5184

%t 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}]

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

%Y Cf A114377, A162681.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 25 2003

%E Sequence data ordered by _Michel Marcus_, Jun 03 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)