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A072026
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Swap twin prime pairs >(3,5) in prime factorization of n.
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5
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1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 13, 12, 11, 10, 21, 16, 19, 18, 17, 28, 15, 26, 23, 24, 49, 22, 27, 20, 31, 42, 29, 32, 39, 38, 35, 36, 37, 34, 33, 56, 43, 30, 41, 52, 63, 46, 47, 48, 25, 98, 57, 44, 53, 54, 91, 40, 51, 62, 61, 84, 59, 58, 45, 64, 77, 78
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OFFSET
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1,2
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COMMENTS
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a(a(n))=n, a self-inverse permutation of natural numbers;
a(n)=n for single primes (A007510) and products of twin prime pairs (A037074).
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LINKS
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Table of n, a(n) for n=1..66.
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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Multiplicative with a(p) = (if p<=3 then p else (if p+2 is prime then p+2 else (if p-2 is prime then p-2 else p))), p prime.
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EXAMPLE
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a(143)=a(11*13)=a(11)*a(13)=13*11=143; a(77)=a(7*11)=a(7)*a(11)=5*13=65.
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MATHEMATICA
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a[n_] := Product[{p, e} = pe; If[p <= 3, p, If[PrimeQ[p+2], p+2, If[PrimeQ[p-2], p-2, p]]]^e, {pe, FactorInteger[n]}];
Array[a, 100] (* Jean-François Alcover, Nov 20 2021 *)
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CROSSREFS
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Cf. A072027, A001359, A006512, A072028, A072029, A061898, A064505.
Sequence in context: A331275 A072028 A269377 * A332213 A235199 A270426
Adjacent sequences: A072023 A072024 A072025 * A072027 A072028 A072029
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KEYWORD
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nonn,mult
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AUTHOR
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Reinhard Zumkeller, Jun 07 2002
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STATUS
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approved
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