A234747 Self-inverse and multiplicative permutation of natural numbers, A091202-conjugate of Blue code: a(n) = A091203(A193231(A091202(n))).

0, 1, 3, 2, 9, 5, 6, 11, 27, 4, 15, 7, 18, 13, 33, 10, 81, 19, 12, 17, 45, 22, 21, 37, 54, 25, 39, 8, 99, 43, 30, 41, 243, 14, 57, 55, 36, 23, 51, 26, 135, 31, 66, 29, 63, 20, 111, 59, 162, 121, 75, 38, 117, 61, 24, 35, 297, 34, 129, 47, 90, 53, 123, 44, 729

Offset: 0

Author

Antti Karttunen, Dec 31 2013

Keywords

• nonn
• mult
• look

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.

Examples

			Example of multiplicativity: a(7)=11, a(23)=37, a(7*23) = a(161) = a(7)*a(23) = 11*37 = 407.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index to divisibility sequences
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A091202, A091203, A193231, A234751.

See A234748 for a variant.

Programs

Scheme

(define (A234747 n) (A091203 (A193231 (A091202 n))))

Formula

a(n) = A091203(A193231(A091202(n))).

Completely multiplicative with p_i = p_{A234751(i)} (where p_i stands for the i-th prime, A000040(i)), and a(x*y) = a(x)*a(y) for x, y > 0.