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

%I A061754 #13 Sep 08 2022 08:45:03
%S A061754 23,29,35,39,44,47,53,55,59,62,63,69,71,74,76,79,80,83,87,89,90,95,97,
%T A061754 98,99,103,104,107,109,111,116,118,119,124,125,127,129,131,132,134,
%U A061754 135,139,142,143,146,149,151,152,153,155,159,160,161,164,167,168,169,170
%N A061754 Numbers k such that k! is divisible by (k+1)^6.
%H A061754 Robert Israel, <a href="/A061754/b061754.txt">Table of n, a(n) for n = 1..10000</a>
%p A061754 filter:= proc(n) local q,t,p,i,w,F;
%p A061754   F:= ifactors(n+1)[2];
%p A061754   for q in F do
%p A061754     p:= q[1];
%p A061754     t:= 0:
%p A061754     for i from 1 do
%p A061754       w:= floor(n/p^i);
%p A061754       if w = 0 then return false fi;
%p A061754       t:= t+w;
%p A061754       if t >= 6*q[2] then break fi;
%p A061754     od;
%p A061754   od;
%p A061754   true
%p A061754 end proc:
%p A061754 select(filter, [$1..200]); # _Robert Israel_, Jul 01 2018
%t A061754 Select[Range[200], IntegerQ[ #!/(# + 1)^6] &]
%o A061754 (PARI) isok(n) = !(n! % (k+1)^6); \\ _Michel Marcus_, Jul 02 2018
%o A061754 (Magma) [n: n in [1..200]| Factorial(n) mod (n+1)^6 eq 0]; // _Vincenzo Librandi_, Jul 02 2018
%K A061754 nonn
%O A061754 1,1
%A A061754 _Robert G. Wilson v_, Jun 21 2001