OFFSET
1,8
COMMENTS
First differs from A050361 at n = 64.
From Amiram Eldar, Sep 08 2023: (Start)
A coreful divisor d of a number n is a divisor with the same set of distinct prime factors as n. (End)
Also, the number of divisors of n that are cubefull exponentially odd numbers (A335988). - Amiram Eldar, Feb 11 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = floor((e+1)/2).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/(p*(p^2-1))) = 1.231291... (A065487). - Amiram Eldar, Sep 10 2022
a(n) = A046951(A350390(n)) (the number of squares dividing the largest exponentially odd divisor of n). - Amiram Eldar, Sep 01 2023
From Amiram Eldar, Sep 08 2023: (Start)
Dirichlet g.f.: zeta(s) * zeta(2*s) * Product_{p prime} (1 - 1/p^(2*s) + 1/p^(3*s)). (End)
MATHEMATICA
fun[p_, e_] := Floor[(e+1)/2]; a[n_] := Times@@(fun@@@FactorInteger[n]); Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> (x+1)\2, factor(n)[, 2])); \\ Amiram Eldar, Sep 01 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 07 2019
EXTENSIONS
Name corrected by Amiram Eldar, Sep 08 2023
STATUS
approved