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A159836 Integers n such that the orbit n, f(n), f(f(n)), ... is eventualy periodic with period 2, where f(n)=Product[a(k)^p(k)] when n has the prime factorization n=Product[p(k)^a(k)]. 0
8, 9, 18, 24, 25, 32, 36, 40, 45, 49, 50, 56, 63, 64, 75, 81, 88, 90, 96, 98, 99, 100, 104, 117, 120, 121, 125, 126, 128, 136, 144, 147, 150, 152, 153, 160, 162, 168, 169, 171, 175, 180, 184, 192, 196, 198, 200 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

It is proved in the reference that for every positive integer n the orbit n, f(n), f(f(n)), ... is eventually periodic with period 1 or 2.

REFERENCES

Problem 11315, American Mathematical Monthly, May 2009, page 470.

CROSSREFS

A008477, A008478

Sequence in context: A057104 A095191 A050706 * A069809 A067544 A022313

Adjacent sequences:  A159833 A159834 A159835 * A159837 A159838 A159839

KEYWORD

nonn

AUTHOR

John W. Layman (layman(AT)math.vt.edu), Apr 23 2009

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Last modified February 16 20:57 EST 2012. Contains 205967 sequences.