OFFSET
1,2
COMMENTS
First differs from A331737 at n = 16.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^e if e is odd and p^(e-1) otherwise.
a(n) = n/A336643(n).
a(n) = n if and only if n is an exponentially odd number (A268335).
Sum_{k=1..n} a(k) ~ (1/2)*c*n^2, where c = Product_{p prime} 1-(p-1)/(p^2*(p+1)) = 0.8073308216... (A306071).
Dirichlet g.f.: zeta(2*s-2) * Product_{p prime} (1 + 1/p^(s-1) - 1/p^(2*s-2) + 1/p^(2*s-1)). - Amiram Eldar, Sep 18 2023
MATHEMATICA
f[p_, e_] := If[OddQ[e], p^e, p^(e - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(Python)
from math import prod
from sympy.ntheory.factor_ import primefactors, core
def A350390(n): return n*core(n)//prod(primefactors(n)) # Chai Wah Wu, Dec 30 2021
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(f[i, 2] - !(f[i, 2]%2))); } \\ Amiram Eldar, Sep 18 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 28 2021
STATUS
approved