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A160199
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Product of non-exponential divisors of n.
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0
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1, 1, 1, 1, 1, 6, 1, 4, 1, 10, 1, 24, 1, 14, 15, 8, 1, 54, 1, 40, 21, 22, 1, 2304, 1, 26, 9, 56, 1, 27000, 1, 512, 33, 34, 35, 216, 1, 38, 39, 6400, 1, 74088, 1, 88, 135, 46, 1, 73728, 1, 250, 51, 104, 1, 26244, 55, 12544, 57, 58, 1, 25920000, 1, 62, 189, 512, 65, 287496, 1
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OFFSET
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1,6
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COMMENTS
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The non-exponential divisors of n are those divisors of n that are not exponential divisors of n.
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LINKS
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Eric Weisstein's World of Mathematics, e-Divisor
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FORMULA
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EXAMPLE
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The divisors of 6 are 1, 2, 3, 6. The only exponential divisor of 6 is 6, hence a(6) = 1*2*3 = 6.
The divisors of 16 are 1, 2, 4, 8, 16. The exponential divisors of 16 are 2, 4, 16, hence a(16) = 1*8 = 8.
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PROG
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(Magma) [1] cat [ &*[ d: d in Divisors(n) | exists(t) { p: p in P | v eq 0 or e mod v gt 0 where v is Valuation(d, p) where e is Valuation(n, p) } where P is PrimeDivisors(n) ]: n in [2..67] ]; // Klaus Brockhaus, May 26 2009
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CROSSREFS
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Cf. A007955 (product of divisors of n), A157488 (product of exponential divisors of n).
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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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