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A272880
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Number of integers in [prime(n), 2*prime(n)] with maximal number of divisors.
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1
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1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Let n=3, prime(n)=5. In the interval [5,10] we have 3 numbers {6,8,10} with maximal number of divisors in this interval (4). So, a(3)=3.
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MATHEMATICA
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a[n_] := Tally[Sort@ DivisorSigma[0, Range[#, 2 #]&@ Prime@n]][[-1, 2]]; Array[a, 87] (* Giovanni Resta, May 08 2016 *)
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PROG
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(PARI) a(n) = {my(nb = 2*prime(n) - prime(n) + 1); my(vd = vector(nb, i, numdiv(prime(n)+i-1))); my(vmax = vecmax(vd)); #select(x->x == vmax, vd); } \\ Michel Marcus, May 09 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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