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Compare with the completely multiplicative, self-inverse A225546, which also maps 2^e to the squarefree number A019565(e). However, this sequence maps p^e to the same squarefree number for every prime p, whereas A225546 maps the e-th power of progressively larger primes to progressively greater powers of A019565(e).
approved
editing
proposed
approved
editing
proposed
Compare with the completely multiplicative involution, , self-inverse A225546, which also maps each power of 2 ^e to the same squarefree number that A019565(e). However, this sequence does, but maps powers p^e to the same squarefree number for every prime p, whereas A225546 maps the e-th power of progressively larger primes to progressively greater powers of squarefree numbersA019565(e).
From Peter Munn, Apr 06 2021: (Start)
a(n) is determined by the prime signature of n. Powers of squarefree numbers are mapped to powers of squarefree numbers. - _Peter Munn_, Mar 26 2021
Compare with the completely multiplicative involution, A225546, which maps each power of 2 to the same squarefree number that this sequence does, but maps powers of larger primes to greater powers of squarefree numbers.
Both sequences map powers of squarefree numbers to powers of squarefree numbers.
(End)
a(n) is determined by the prime signature of n. Powers of squarefree numbers are mapped to powers of squarefree numbers. - Peter Munn, Mar 26 2021
<a href="/index/Pri#prime_signature">Index entries for sequences related to prime signature</a>
For n >= 3, a(n) < n.