A181351 Exchange 2 and 5 in the prime factorization of n.

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

Offset

1,2

Comments

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers.

Formula

Dirichlet g.f.: zeta(s-1)*(2^s-2)*(5^s-5)/((2^s-5)*(5^s-2)). - Amiram Eldar, Jul 18 2023

Example

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

Mathematica

a[n_] := n * Times @@ ({5/2, 2/5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* Amiram Eldar, Jul 18 2023 *)

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: A146317 A168253 A357756 * A266385 A354091 A032532

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