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A061754 Numbers k such that k! is divisible by (k+1)^6. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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] &]

PROG

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

(MAGMA) [n: n in [1..200]| Factorial(n) mod (n+1)^6 eq 0]; // Vincenzo Librandi, Jul 02 2018

CROSSREFS

Sequence in context: A214754 A153631 A082943 * A180066 A101784 A101802

Adjacent sequences:  A061751 A061752 A061753 * A061755 A061756 A061757

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 21 2001

STATUS

approved

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Last modified July 23 22:49 EDT 2019. Contains 325278 sequences. (Running on oeis4.)