A337611 Positive integers m such that A126288^k(m) = m for some positive integer k.

2, 3, 6, 10, 14, 20, 22, 26, 28, 38, 44, 46, 52, 76, 78, 88, 94, 102, 105, 114, 116, 117, 136, 138, 152, 171, 186, 187, 195, 207, 212, 247, 248, 266, 282, 284, 285, 296, 304, 322, 333, 354, 366, 369, 387, 402, 403, 407, 414, 423, 425, 426, 430, 437, 442, 468

Offset: 1

Author

Ely Golden, Sep 05 2020

Keywords

• nonn

Comments

A126288^k(m) means apply A126288 to m k times.

Equivalently, the numbers that belong to a cycle under the map x -> A126288(x).

2 and 3 are the only primes in this sequence.

Examples

			3 is a term since A126288(A126288(3)) = A126288(2) = 3.
		

Links

• Ely Golden, Table of n, a(n) for n = 1..7144
• Ely Golden, Python program for (naïvely) generating terms of this sequence

Crossrefs

Cf. A337609, A337610, A337612, A126288, A052126.

Programs

PARI

gpf(n) = vecmax(factor(n)[,1]);
f(n) = if (n==1, 2, n*gpf(n+1)/gpf(n)); \\ A126288
incycle(n, list) = {my(v=Vec(list)); #select(x->(x==n), v);}
cycle(n) = {my(list = List(), repeat=1); while(repeat, n = f(n); if (incycle(n, list), repeat=0); listput(list, n);); list;}
isok(n) = {my(list = cycle(n)); incycle(n, list);} \\ Michel Marcus, Sep 08 2020

Formula

For any term m, gcd {m, A126288(m), A126288(A126288(m)), ...} = A052126(m).