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 A261193 a(n) = n! - 2. 1
 -1, -1, 0, 4, 22, 118, 718, 5038, 40318, 362878, 3628798, 39916798, 479001598, 6227020798, 87178291198, 1307674367998, 20922789887998, 355687428095998, 6402373705727998, 121645100408831998, 2432902008176639998, 51090942171709439998, 1124000727777607679998 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS It is possible to prove that, if gcd(k,a,b) = 1, then k^a + a^b + b^k = n! can be solved only if a = b = 1, thus k = n! - 2 for every n > 2. LINKS M Cipu, F. Luca and M. Mignotte, Solutions of the diophantine equation x^y+y^z+z^x=n!, Glasgow Mathematical Journal, 50(2008), 217-232. FORMULA a(n) = A000142(n) - 2 = A033312(n) - 1. E.g.f.: 1/(1-x) - 2*exp(x). - Alois P. Heinz, Sep 10 2015 MAPLE A261193:=n->n!-2: seq(A261193(n), n=1..20); # Wesley Ivan Hurt, Aug 13 2015 MATHEMATICA Table[n! - 2, {n, 20}] (* Wesley Ivan Hurt, Aug 13 2015 *) PROG (MAGMA) [Factorial(n)-2 : n in [1..20]]; // Wesley Ivan Hurt, Aug 13 2015 (PARI) a(n)=n!-2 \\ Charles R Greathouse IV, Aug 28 2015 CROSSREFS Cf. A000142, A033312. Sequence in context: A245087 A155596 A244900 * A025569 A098834 A065983 Adjacent sequences:  A261190 A261191 A261192 * A261194 A261195 A261196 KEYWORD sign,easy AUTHOR Marco Ripà, Aug 11 2015 EXTENSIONS a(0)-a(1) corrected by David A. Corneth, Sep 10 2015 STATUS approved

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)