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A117134
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Greatest k such that n^k divides (n^2)!.
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1
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3, 4, 7, 6, 17, 8, 21, 20, 24, 12, 70, 14, 32, 55, 63, 18, 80, 20, 99, 73, 48, 24, 191, 78, 56, 121, 130, 30, 224, 32, 204, 108, 72, 203, 323, 38, 80, 126, 398, 42, 293, 44, 193, 505, 96, 48, 575, 200, 312, 162, 225, 54, 485, 302, 522, 180, 120, 60, 898, 62, 128, 660, 682
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OFFSET
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2,1
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COMMENTS
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If p is prime, a(p) = p+1, a(p^2) = floor((p^3 + p^2 + p + 1)/2).
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REFERENCES
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Thread "100!" in rec.puzzles newsgroup, April 2007
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LINKS
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EXAMPLE
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a(3)=4 because (3^2)! = 362880 = 3^4 * 4480 and 4480 is not divisible by 3.
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MAPLE
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seq(ordp((n^2)!, n), n=2..50);
# Alternative:
f:= proc(n) local F, m, t, v, j;
F:= ifactors(n)[2];
m:= infinity;
for t in F do
v:= add(floor(n^2/t[1]^j), j=1..ceil(log[t[1]](n^2)));
m:= min(m, floor(v/t[2]));
od;
m
end proc:
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MATHEMATICA
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gkn[n_]:=Module[{c=(n^2)!, k}, k=Floor[Log[c]/Log[n]]; While[!Divisible[ c, n^k], k--]; k]; Array[gkn, 70, 2] (* Harvey P. Dale, Sep 14 2012 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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