A061759 Numbers k such that k! is divisible by (k+1)^11.

59, 71, 79, 83, 89, 95, 99, 104, 107, 111, 119, 125, 127, 131, 134, 139, 143, 146, 149, 153, 155, 159, 161, 164, 167, 174, 175, 179, 181, 188, 191, 194, 195, 197, 199, 203, 207, 209, 215, 219, 220, 223, 224, 227, 230, 233, 237, 239, 241, 242, 244, 246, 249

Offset: 1

Author

Robert G. Wilson v, Jun 21 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..2000

Programs

Magma

[n: n in [1..250]| Factorial(n) mod (n+1)^11 eq 0]; // Vincenzo Librandi, Jul 02 2018

Maple

filter:= proc(n) local q,t,p,i,w,F;
  F:= ifactors(n+1)[2];
  for q in F do
    p:= q[1];
    t:= 0:
    for i from 1 do
      w:= floor(n/p^i);
      if w = 0 then return false fi;
      t:= t+w;
      if t >= 11*q[2] then break fi;
    od;
  od;
  true
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 01 2018

Mathematica

Select[Range[250], IntegerQ[ #!/(# + 1)^11] &]

PARI

{ n=0; f=1; for (a=1, 3879, f*=a; if (f%(a + 1)^11 == 0, write("b061759.txt", n++, " ", a)) ) } \\ Harry J. Smith, Jul 27 2009