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A303278
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If n = Product_j p_j^k_j where the p_j are distinct primes then a(n) = (Product_j k_j)^(Product_j p_j).
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3
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1, 1, 1, 4, 1, 1, 1, 9, 8, 1, 1, 64, 1, 1, 1, 16, 1, 64, 1, 1024, 1, 1, 1, 729, 32, 1, 27, 16384, 1, 1, 1, 25, 1, 1, 1, 4096, 1, 1, 1, 59049, 1, 1, 1, 4194304, 32768, 1, 1, 4096, 128, 1024, 1, 67108864, 1, 729, 1, 4782969, 1, 1, 1, 1073741824, 1, 1, 2097152, 36, 1, 1, 1, 17179869184, 1, 1, 1, 46656, 1, 1, 32768
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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a(p^k) = k^p where p is a prime.
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EXAMPLE
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a(36) = a(2^2 * 3^2) = (2*2)^(2*3) = 4^6 = 4096.
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MATHEMATICA
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Table[Times@@Transpose[FactorInteger[n]][[2]]^Last[Select[Divisors[n], SquareFreeQ]], {n, 75}]
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PROG
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(PARI) a(n) = my(f=factor(n)); factorback(f[, 2])^factorback(f[, 1]); \\ Michel Marcus, Apr 21 2018
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CROSSREFS
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Cf. A000026, A000142, A005117 (indices of ones), A005361, A007947, A008477, A034386, A039696, A135291, A285769, A303277.
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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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