A262599 Lexicographically earliest sequence of distinct terms such that, for any n > 0, phi(a(n)) = phi(n) (where phi denotes the Euler totient function), and a(n) > n if possible.

2, 1, 4, 6, 8, 3, 9, 10, 14, 12, 22, 5, 21, 18, 16, 20, 32, 7, 27, 24, 26, 11, 46, 30, 33, 28, 38, 36, 58, 15, 62, 34, 44, 40, 39, 42, 57, 54, 45, 48, 55, 13, 49, 50, 52, 23, 94, 60, 86, 66, 64, 56, 106, 19, 75, 70, 63, 29, 118, 17, 77, 31, 74, 68, 104, 25

Offset: 1

Author

Paul Tek, Sep 25 2015

Keywords

• nonn

Comments

This is a permutation of the positive integers, with inverse A262603.

If the Carmichael's totient function conjecture is true, then this sequence has no fixed point.

For any n > 0, the orbit of n is finite, with length A066412(n).

Examples

			phi(n) = 6 iff n is in { 7, 9, 14, 18 }.
Hence: a(7) = 9, a(9) = 14, a(14) = 18, a(18) = 7.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, C program for this sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A049283, A066412, A066659, A262603 (inverse).

Programs

C

// See Links section for C program.

Formula

a(n) = max(A066659(n), A049283(A000010(n))), for any n > 0.