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A072027 Swap (2,3) and all twin prime pairs >(3,5) in prime factorization of n. 3
1, 3, 2, 9, 7, 6, 5, 27, 4, 21, 13, 18, 11, 15, 14, 81, 19, 12, 17, 63, 10, 39, 23, 54, 49, 33, 8, 45, 31, 42, 29, 243, 26, 57, 35, 36, 37, 51, 22, 189, 43, 30, 41, 117, 28, 69, 47, 162, 25, 147, 38, 99, 53, 24, 91, 135, 34, 93, 61, 126, 59, 87, 20, 729, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(a(n))=n, self-inverse permutation of natural numbers; a(n)=n for single primes (A007510) and products of twin prime pairs (A037074).

LINKS

Table of n, a(n) for n=1..65.

Index entries for sequences that are permutations of the natural numbers

FORMULA

Multiplicative with a(p) = (if p<=3 then 5-p else (if p+2 is prime then p+2 else (if p-2 is prime then p-2 else p))), p prime.

EXAMPLE

a(143)=a(11*13)=a(11)*a(13)=13*11=143; a(77)=a(7*11)=a(7)*a(11)=5*13=65.

CROSSREFS

Cf. A072026, A001359, A006512, A072028, A072029, A061898, A064505.

Sequence in context: A011323 A227630 A286251 * A061898 A021756 A274925

Adjacent sequences:  A072024 A072025 A072026 * A072028 A072029 A072030

KEYWORD

nonn,mult

AUTHOR

Reinhard Zumkeller, Jun 07 2002

STATUS

approved

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Last modified November 19 16:10 EST 2017. Contains 294936 sequences.