OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^(1 + floor(e/3)). - Amiram Eldar, Jul 13 2022
Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(5)/2) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 2/p^5 + 1/p^6) = 0.3643121583... . - Amiram Eldar, Nov 13 2022
MAPLE
with(NumberTheory): seq(LargestNthPower(n, 3)*Radical(n), n=1..69);
MATHEMATICA
f[p_, e_] := p^(1 + Floor[e/3]); a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 13 2022 *)
PROG
(Python)
from math import prod
from sympy import factorint
def A355263(n): return prod(p**(e//3+1) for p, e in factorint(n).items()) # Chai Wah Wu, Jul 13 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Peter Luschny, Jul 12 2022
STATUS
approved