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

Author

Jonathan Vos Post, Jan 29 2011

Keywords

• nonn
• easy
• mult

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).

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Cf. A064614.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

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