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

%I A061759 #15 Sep 08 2022 08:45:03
%S A061759 59,71,79,83,89,95,99,104,107,111,119,125,127,131,134,139,143,146,149,
%T A061759 153,155,159,161,164,167,174,175,179,181,188,191,194,195,197,199,203,
%U A061759 207,209,215,219,220,223,224,227,230,233,237,239,241,242,244,246,249
%N A061759 Numbers k such that k! is divisible by (k+1)^11.
%H A061759 Harry J. Smith, <a href="/A061759/b061759.txt">Table of n, a(n) for n = 1..2000</a>
%p A061759 filter:= proc(n) local q,t,p,i,w,F;
%p A061759   F:= ifactors(n+1)[2];
%p A061759   for q in F do
%p A061759     p:= q[1];
%p A061759     t:= 0:
%p A061759     for i from 1 do
%p A061759       w:= floor(n/p^i);
%p A061759       if w = 0 then return false fi;
%p A061759       t:= t+w;
%p A061759       if t >= 11*q[2] then break fi;
%p A061759     od;
%p A061759   od;
%p A061759   true
%p A061759 end proc:
%p A061759 select(filter, [$1..1000]); # _Robert Israel_, Jul 01 2018
%t A061759 Select[Range[250], IntegerQ[ #!/(# + 1)^11] &]
%o A061759 (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
%o A061759 (Magma) [n: n in [1..250]| Factorial(n) mod (n+1)^11 eq 0]; // _Vincenzo Librandi_, Jul 02 2018
%K A061759 nonn
%O A061759 1,1
%A A061759 _Robert G. Wilson v_, Jun 21 2001