|
%I #16 Jan 20 2019 16:38:44
%S 241231,7057861,21166951,52066891,216295321,654480151,1619368381,
%T 2411089396,3486017011,6776093041,12182173471,20592045301,26260194241,
%U 33113005531,51096161161,76160729191,110218336621,131302849486
%N Integers of the form x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1 with x > 0.
%C Generating polynomial is Schur's polynomial of 5-degree. Schur's polynomials n degree are n-th first term of series expansion of e^x function. All polynomials are non-reducible and belonging to the An alternating Galois transitive group if n is divisible by 4 or to Sn symmetric Galois Group in other case (proof Schur, 1930).
%H G. C. Greubel, <a href="/A127881/b127881.txt">Table of n, a(n) for n = 1..5000</a>
%t a = {}; Do[If[IntegerQ[1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120], AppendTo[a, 1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120]], {x, 1, 1000}]; a
%t Select[Table[ x^5/120+x^4/24+x^3/6+x^2/2+x+1,{x,450}],IntegerQ] (* _Harvey P. Dale_, Jan 20 2019 *)
%o (PARI) for(x=1,500,y=x^5+5*x^4+20*x^3+60*x^2+120*x+120;if(y%120==0,print1(y/120, ", "))) \\ _Michael B. Porter_, Jan 29 2010
%o (PARI) isA127881(n)={local(r);r=0;fordiv(120*n-120,x,if(x^5/120+x^4/24+x^3/6+x^2/2+x+1==n,r=1));r} \\ _Michael B. Porter_, Jan 29 2010
%Y Cf. A127873, A127874, A127875, A127876, A127877, A127878, A127879, A127880, A127882, A127883, A127884.
%K nonn
%O 1,1
%A _Artur Jasinski_, Feb 04 2007
|
