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A061112
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a(n) is the minimum number of divisors for any composite between prime(n) and prime(n+1).
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6
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3, 4, 3, 6, 4, 6, 4, 3, 8, 4, 4, 8, 4, 3, 4, 12, 4, 4, 12, 4, 4, 4, 4, 6, 8, 4, 12, 4, 3, 4, 4, 8, 4, 12, 4, 4, 4, 3, 4, 18, 4, 14, 4, 12, 4, 4, 4, 12, 8, 4, 20, 4, 4, 4, 4, 16, 4, 4, 8, 3, 4, 4, 16, 4, 4, 4, 4, 12, 8, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 24, 4, 20, 4, 8, 4, 4, 4, 16, 4, 4, 4, 4, 4, 4, 4, 4
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) = Min_{c=prime(n)+1..prime(n+1)-1} tau(c) where tau(c) is the number of divisors of c.
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EXAMPLE
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prime(30)=113 is followed by 13 composites; their numbers of divisors are {8, 4, 6, 6, 4, 4, 16, 3, 4, 4, 6, 4, 12}. The smallest is 3, so a(30)=3. [corrected by Jon E. Schoenfield, Sep 20 2022]
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MATHEMATICA
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Array[Min@ DivisorSigma[0, Range[#1 + 1, #2 - 1]] & @@ Prime[# + {0, 1}] &, 95, 2] (* Michael De Vlieger, Aug 10 2023 *)
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PROG
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(PARI) { n=-1; q=3; m=10^6; forprime (p=5, prime(1003), a=m; for (i=q + 1, p - 1, a=min(numdiv(i), a)); q=p; write("b061112.txt", n++, " ", a) ) } \\ Harry J. Smith, Jul 19 2009
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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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