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A242457
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Least number k such that k!/n is prime, or 0 if no such number exists.
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2
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2, 3, 3, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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a(n) <= n + 2 for all n > 0.
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LINKS
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EXAMPLE
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a(3) = 3 because 3!/3 = 6/3 = 2, which is prime.
a(4) = 0 because there is no k such that k!/4 is a prime. For all k > 3, k! has 24 as a divisor, so therefore k!/4 has 6 as a divisor and is therefore certainly composite.
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MAPLE
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N:= 7: # to get all a(n) for n <= N!
A:= Array(1..N!):
for k from 1 to N do
for p in select(isprime, [$2..k]) do
if A[k!/p] = 0 then A[k!/p]:= k fi
od
od:
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PROG
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(PARI)
a(n)=for(k=1, n+2, s=k!/n; if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<100, print1(a(n), ", "); n++)
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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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