A261193 a(n) = n! - 2.

-1, -1, 0, 4, 22, 118, 718, 5038, 40318, 362878, 3628798, 39916798, 479001598, 6227020798, 87178291198, 1307674367998, 20922789887998, 355687428095998, 6402373705727998, 121645100408831998, 2432902008176639998, 51090942171709439998, 1124000727777607679998

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

Table of n, a(n) for n=0..22.

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