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

1,1

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.

Links

Ely Golden, Table of n, a(n) for n = 1..7144

Ely Golden, Python program for (naïvely) generating terms of this sequence

Formula

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A355509 A084396 A090035 * A325724 A111467 A215891

Adjacent sequences: A337608 A337609 A337610 * A337612 A337613 A337614

Keyword

nonn

Author

Ely Golden, Sep 05 2020

Status

approved