n > 4. This was proven in 1985 for all sufficiently large integers by András Sárközy, and for all integers > 4 in 1996 by Olivier Ramaré and Andrew Granville. Squarefree core Let us call "t-free" a positive integer that has no t-th power in its divisors. In particular, the 2-free integers are the square-free integers. The multiplicative function maps every positive integer n to the quotient of n by its largest divisor that is a t-th power. That is, The integer is t-free, and every t-free integer is mapped to itself by the function The Dirichlet generating function of the sequence is . See also (t=2), (t=3) and (t=4). Notes References Number theory Integer sequences