Square-free Integer - Squarefree Core

Squarefree Core

The multiplicative function is defined to map positive integers n to t-free numbers by reducing the exponents in the prime power representation modulo t:

The value set of, in particular, are the square-free integers. Their Dirichlet generating functions are

$\sum_{n\ge 1}\frac{\mathrm{core}_t(n)}{n^s} = \frac{\zeta(ts)\zeta(s-1)}{\zeta(ts-t)}$ .

OEIS representatives are A007913 (t=2), A050985 (t=3) and A053165 (t=4).

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