A061754 Numbers k such that k! is divisible by (k+1)^6.

23, 29, 35, 39, 44, 47, 53, 55, 59, 62, 63, 69, 71, 74, 76, 79, 80, 83, 87, 89, 90, 95, 97, 98, 99, 103, 104, 107, 109, 111, 116, 118, 119, 124, 125, 127, 129, 131, 132, 134, 135, 139, 142, 143, 146, 149, 151, 152, 153, 155, 159, 160, 161, 164, 167, 168, 169, 170

Offset: 1

Author

Robert G. Wilson v, Jun 21 2001

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Magma

[n: n in [1..200]| Factorial(n) mod (n+1)^6 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 >= 6*q[2] then break fi;
    od;
  od;
  true
end proc:
select(filter, [$1..200]); # Robert Israel, Jul 01 2018

Mathematica

Select[Range[200], IntegerQ[ #!/(# + 1)^6] &]

PARI

isok(n) = !(n! % (k+1)^6); \\ Michel Marcus, Jul 02 2018