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 A162681 Numbers k such that k^2 is a sum of three factorials. 1
 2, 3, 6, 7, 29, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The next term after 72 is larger than 10^40 (if it exists). - R. J. Mathar, Jul 16 2009 LINKS Table of n, a(n) for n=1..6. EXAMPLE 2^2 = 1! + 1! + 2!; 3^2 = 1! + 2! + 3!; 6^2 = 3! + 3! + 4!; 7^2 = 1! + 4! + 4!; 29^2 = 1! + 5! + 6!; 72^2 = 4! + 5! + 7!. MAPLE s := 10^40 ; sqr := s^2 : for a from 1 do if a! > sqr then break; fi; for b from a do if a!+b! > sqr then break; fi; for c from b do if a!+b!+c! > sqr then break; fi; if issqr(a!+b!+c!) then print( sqrt(a!+b!+c!)); fi; od: od: od: # R. J. Mathar, Jul 16 2009 w := 7: f := proc (x, y, z) options operator, arrow: sqrt(factorial(x)+factorial(y)+factorial(z)) end proc: A := {}: for x to w do for y to w do for z to w do if type(f(x, y, z), integer) = true then A := `union`(A, {f(x, y, z)}) else end if end do end do end do: A; # Emeric Deutsch, Aug 03 2009 MATHEMATICA \$MaxExtraPrecision=Infinity; lst={}; Do[Do[Do[x=(a!+b!+c!)^(1/2); If[x==IntegerPart[x], AppendTo[lst, x]], {c, b, 2*4!}], {b, a, 2*4!}], {a, 2*4!}]; Union[lst] CROSSREFS Cf. A065433, A082875. Sequence in context: A073317 A064731 A159069 * A070301 A329294 A291659 Adjacent sequences: A162678 A162679 A162680 * A162682 A162683 A162684 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Jul 10 2009 EXTENSIONS Definition rephrased by R. J. Mathar, Jul 16 2009 STATUS approved

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Last modified March 4 12:21 EST 2024. Contains 370532 sequences. (Running on oeis4.)