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A072029 Swap twin prime pairs of form (4*k+3,4*(k+1)+1) in prime factorization of n. 4
1, 2, 5, 4, 3, 10, 7, 8, 25, 6, 13, 20, 11, 14, 15, 16, 17, 50, 19, 12, 35, 26, 23, 40, 9, 22, 125, 28, 29, 30, 31, 32, 65, 34, 21, 100, 37, 38, 55, 24, 41, 70, 43, 52, 75, 46, 47, 80, 49, 18, 85, 44, 53, 250, 39, 56, 95, 58, 61, 60, 59, 62, 175, 64, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(a(n))=n, a self-inverse permutation of natural numbers.

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 mod 4 = 3 and p+2 is prime then p+2 else (if p mod 4 = 1 and p-2 is prime then p-2 else p)), p prime.

EXAMPLE

a(42) = a(2*3*7) = a(2)*a(3)*a(7) = a(2)*a(4*0+3)*a(7) = 2*(4*1+1)*7 = 2*5*7 = 70.

MATHEMATICA

a[n_] := Product[{p, e} = pe; Which[

     Mod[p, 4] == 3 && PrimeQ[p + 2], p + 2,

     Mod[p, 4] == 1 && PrimeQ[p - 2], p - 2,

     True, p]^e, {pe, FactorInteger[n]}];

Array[a, 100] (* Jean-François Alcover, Nov 21 2021 *)

CROSSREFS

Cf. A072028, A071698, A071699, A072026, A072027, A061898, A064505.

Sequence in context: A266403 A266415 A132664 * A309734 A309668 A238758

Adjacent sequences:  A072026 A072027 A072028 * A072030 A072031 A072032

KEYWORD

nonn,mult

AUTHOR

Reinhard Zumkeller, Jun 07 2002

STATUS

approved

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Last modified December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)