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A181351
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Exchange 2 and 5 in the prime factorization of n.
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2
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1, 5, 3, 25, 2, 15, 7, 125, 9, 10, 11, 75, 13, 35, 6, 625, 17, 45, 19, 50, 21, 55, 23, 375, 4, 65, 27, 175, 29, 30, 31, 3125, 33, 85, 14, 225, 37, 95, 39, 250, 41, 105, 43, 275, 18, 115, 47, 1875, 49, 20, 51, 325, 53, 135, 22, 875, 57, 145, 59, 150, 61, 155, 63
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OFFSET
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1,2
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COMMENTS
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A self-inverse permutation of the natural numbers.
a(1) = 1, a(2) = 5, a(5) = 2, a(p) = p for primes p = 3 and p > 5 and a(u * v) = a(u) * a(v) for u, v > 0.
A permutation of the natural numbers: a(a(n)) = n for all n and a(n) = n if and only if n = 10^k * m for k >= 0 and m > 0 with GCD(m, 10) = 1. This is to (2,5) as A064614 is to (2,3).
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LINKS
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FORMULA
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Dirichlet g.f.: zeta(s-1)*(2^s-2)*(5^s-5)/((2^s-5)*(5^s-2)). - Amiram Eldar, Jul 18 2023
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EXAMPLE
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a(15) = a(3*5) = a(3)*a(5) = 3*2 = 6.
a(16) = a(2^4) = a(2^4 = 5^4 = 625.
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MATHEMATICA
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a[n_] := n * Times @@ ({5/2, 2/5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* Amiram Eldar, Jul 18 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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