A245453 Self-inverse and multiplicative permutation of natural numbers, A235041-conjugate of balanced bit-reverse: a(n) = A235042(A057889(A235041(n))).

0, 1, 2, 3, 4, 19, 6, 7, 8, 9, 38, 13, 12, 11, 14, 57, 16, 59, 18, 5, 76, 21, 26, 53, 24, 361, 22, 27, 28, 109, 114, 31, 32, 39, 118, 133, 36, 41, 10, 33, 152, 37, 42, 103, 52, 171, 106, 61, 48, 49, 722, 177, 44, 23, 54, 247, 56, 15, 218, 17, 228, 47, 62, 63, 64

Offset: 0

Author

Antti Karttunen, Aug 07 2014

Keywords

• nonn
• mult

Comments

a(n) has the same prime signature as n: The permutation maps primes to primes, squares to squares, cubes to cubes, and so on. Permutation A234748 shares the same property.

Examples

			Example of multiplicativity:
a(5)=19, a(11)=13, a(55) = a(5*11) = a(5) * a(11) = 19*13 = 247.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..624
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A057889, A235041, A235042, A234748, A245450, A235027.

Programs

Scheme

(define (A245453 n) (A235042 (A057889 (A235041 n))))

Formula

a(n) = A235042(A057889(A235041(n))).