A248693 Numbers k such that the product of factorials of proper divisors of k does not divide k!.
24, 30, 36, 40, 48, 54, 60, 72, 80, 84, 90, 96, 100, 102, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252, 260, 264, 270, 272, 276, 280, 288, 294, 300, 306, 308, 312, 320
Offset: 1
Examples
Let Q(n) = n!/(product of the proper divisors of n). Then Q(n) an integer for n = 1..23, as indicated by the following list of Q(n) for n = 1..24: 1, 2, 6, 12, 120, 60, 5040, 840, 60480, 15120, 39916800, 2310, 6227020800, 8648640, 1816214400, 10810800, 355687428096000, 2042040, 121645100408832000, 116396280, 1689515283456000, 14079294028800, 25852016738884976640000, 7436429/48.
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Mathematica
d[n_] := Drop[Divisors[n], -1]!; p[n_] := Apply[Times, d[n]] u = Select[Range[25000], ! IntegerQ[#!/p[#]] &]; (* A248693 *) Select[u, OddQ[#] &] (* A248694 *) (* Second program *) Select[Range@ 320, ! Divisible[#!, Times @@ Map[Factorial, Most@ Divisors@ #]] &] (* Michael De Vlieger, Dec 31 2016 *)
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PARI
is(n)=prod(i=2,n-1,i,Mod(n,prod(j=2,-1+#n=divisors(n),n[j]!))) \\ Returns nonzero (actually, Mod(n!,P) where P = product_{d|n, d
Comments