

A181351


Exchange 2 and 5 in the prime factorization of n.


1



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

1,2


COMMENTS

A selfinverse 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).


LINKS

Table of n, a(n) for n=1..63.
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

a(15) = a(3*5) = a(3)*a(5) = 3*2 = 6.
a(16) = a(2^4) = a(2^4 = 5^4 = 625.


PROG

(PARI) a(n)=n*(5/2)^valuation(n, 2)*(2/5)^valuation(n, 5) \\ Charles R Greathouse IV, Dec 07 2011


CROSSREFS

Cf. A064614.
Sequence in context: A290074 A146317 A168253 * A266385 A032532 A111108
Adjacent sequences: A181348 A181349 A181350 * A181352 A181353 A181354


KEYWORD

nonn,easy,mult


AUTHOR

Jonathan Vos Post, Jan 29 2011


EXTENSIONS

a(20) corrected by Charles R Greathouse IV, Dec 07 2011


STATUS

approved



