A360648 Fully multiplicative with a(A027697(k)) = A027699(k) and a(A027699(k)) = A027697(k) for any k > 0.

1, 3, 2, 9, 7, 6, 5, 27, 4, 21, 17, 18, 23, 15, 14, 81, 11, 12, 29, 63, 10, 51, 13, 54, 49, 69, 8, 45, 19, 42, 43, 243, 34, 33, 35, 36, 53, 87, 46, 189, 71, 30, 31, 153, 28, 39, 83, 162, 25, 147, 22, 207, 37, 24, 119, 135, 58, 57, 89, 126, 101, 129, 20, 729

Offset: 1

Author

Rémy Sigrist, Feb 15 2023

Keywords

• nonn
• base
• mult

Comments

In other words, we replace odious prime numbers with evil prime numbers and vice versa.

This sequence is a self-inverse permutation of the positive integers.

Examples

			For n = 84:
- 82 = 2^2 * 3 * 7,
- a(2) = a(A027697(1)) = A027699(1) = 3,
- a(3) = a(A027699(1)) = A027697(1) = 2,
- a(7) = a(A027697(2)) = A027699(2) = 5,
- so a(84) = 3^2 * 2 * 5 = 90.
		

Links

• Rémy Sigrist, Scatterplot of (n, a(n)) such that n, a(n) <= 100000
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A061898, A027697, A027699, A341090.

Programs

PARI

See Links section.