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A337611
Positive integers m such that A126288^k(m) = m for some positive integer k.
4
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.
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
KEYWORD
nonn
AUTHOR
Ely Golden, Sep 05 2020
STATUS
approved