OFFSET
1,64
COMMENTS
The number of divisors of the square root of the largest square dividing n is A046951(n).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) > 1 if and only if n is a bicubeful number (A355265).
Multiplicative with a(p^e) = floor((e+2)/4).
Dirichlet g.f.: zeta(s) * zeta(4*s) * Product_{p prime} (1 - 1/p^(4*s) + 1/p^(6*s)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(4) * Product_{p prime} (1 - 1/p^4 + 1/p^6) = 1.0181534831085... .
MATHEMATICA
f[p_, e_] := Max[1, Floor[(e+2)/4]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> max(1, (x+2)\4), factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 01 2023
EXTENSIONS
Name corrected by Amiram Eldar, Sep 08 2023
STATUS
approved