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A292286
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a(n) = k if the product of the divisors of n is n^k for some integer k, or -1 if no such k exists. For the ambiguous case, define a(1) = 0.
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2
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0, 1, 1, -1, 1, 2, 1, 2, -1, 2, 1, 3, 1, 2, 2, -1, 1, 3, 1, 3, 2, 2, 1, 4, -1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, -1, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, -1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 6, 1, 2, 3, -1, 2, 4, 1, 3, 2, 4, 1, 6, 1, 2, 3, 3, 2, 4, 1, 5, -1, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 3, -1
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OFFSET
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1,6
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COMMENTS
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If the number of divisors (nd) of n > 1 is odd, then a(n) = -1, else a(n) = nd/2. - Michel Marcus, Sep 14 2017
Records occur for A293570(r): 4, 6, 12, 24, 48, 60, 192, 240, 3072, 12288, 196608, 786432, 12582912, 805306368, etc. - Robert G. Wilson v, Oct 10 2017
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LINKS
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FORMULA
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EXAMPLE
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a(10) = 2 because divisors of 10 are 1,2,5,10 with product 100 = 10^2.
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MATHEMATICA
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Table[Boole[n == 1] + If[OddQ@ #, -1, #/2] &@ DivisorSigma[0, n], {n, 100}] (* Michael De Vlieger, Sep 15 2017 *)
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PROG
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(PARI) a(n) = if (n==1, 0, my(nd = numdiv(n)); if (nd % 2, -1, nd/2)); \\ Michel Marcus, Sep 14 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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