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A061754
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Numbers k such that k! is divisible by (k+1)^6.
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8
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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
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OFFSET
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1,1
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LINKS
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MAPLE
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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:
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MATHEMATICA
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Select[Range[200], IntegerQ[ #!/(# + 1)^6] &]
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PROG
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(Magma) [n: n in [1..200]| Factorial(n) mod (n+1)^6 eq 0]; // Vincenzo Librandi, Jul 02 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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