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

1,1

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).

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, C99 program for this sequence

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

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

Prog

(C99) See Links section.

Crossrefs

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

Sequence in context: A335920 A111104 A026190 * A160016 A245089 A335919

Adjacent sequences: A262596 A262597 A262598 * A262600 A262601 A262602

Keyword

nonn

Author

Paul Tek, Sep 25 2015

Status

approved