login
A365680
The number of exponentially squarefree divisors of n.
7
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 5, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 8, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 6, 4, 8, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, 8, 4, 4, 2, 12, 4, 4
OFFSET
1,2
COMMENTS
First differs from A252505 at n = 32.
The number of divisors of n that are exponentially squarefree numbers (A209061), i.e., numbers having only squarefree exponents in their canonical prime factorization.
The sum of these divisors is A365682(n) and the largest of them is A365683(n).
LINKS
FORMULA
Multiplicative with a(p^e) = A013928(e+1) + 1.
a(n) <= A000005(n), with equality if and only if n is a biquadratefree number (A046100).
MATHEMATICA
f[p_, e_] := Count[Range[e], _?SquareFreeQ] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(n) = sum(k=1, n, issquarefree(k)) + 1;
a(n) = vecprod(apply(x -> s(x), factor(n)[, 2]));
CROSSREFS
Similar sequences: A325837, A353898.
Sequence in context: A252505 A365173 A366991 * A325560 A318412 A365208
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 15 2023
STATUS
approved