OFFSET
1,16
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^A081221(e).
a(n) = A365684(n)/n.
a(n) >= 1, with equality if and only if n is an exponentially squarefree number (A209061).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + Sum_{k>=1} (p^f(k) - p^f(k-1))/p^k) = 1.06562841319..., where f(k) = A081221(k) and f(0) = 0.
MATHEMATICA
f[p_, e_] := Module[{k = e}, While[! SquareFreeQ[k], k++]; p^(k-e)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(e) = {my(k = e); while(!issquarefree(k), k++); k - e; };
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 15 2023
STATUS
approved