A337611 - OEIS

%I #22 Oct 07 2020 13:13:14

%S 2,3,6,10,14,20,22,26,28,38,44,46,52,76,78,88,94,102,105,114,116,117,

%T 136,138,152,171,186,187,195,207,212,247,248,266,282,284,285,296,304,

%U 322,333,354,366,369,387,402,403,407,414,423,425,426,430,437,442,468

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

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

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

%C 2 and 3 are the only primes in this sequence.

%H Ely Golden, <a href="/A337611/b337611.txt">Table of n, a(n) for n = 1..7144</a>

%H Ely Golden, <a href="/A337611/a337611_1.py.txt">Python program for (naïvely) generating terms of this sequence</a>

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

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

%o (PARI) gpf(n) = vecmax(factor(n)[,1]);

%o f(n) = if (n==1, 2, n*gpf(n+1)/gpf(n)); \\ A126288

%o incycle(n, list) = {my(v=Vec(list)); #select(x->(x==n), v);}

%o cycle(n) = {my(list = List(), repeat=1); while(repeat, n = f(n); if (incycle(n, list), repeat=0); listput(list, n);); list;}

%o isok(n) = {my(list = cycle(n)); incycle(n, list);} \\ _Michel Marcus_, Sep 08 2020

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

%K nonn

%O 1,1

%A _Ely Golden_, Sep 05 2020