OFFSET
1,2
COMMENTS
The largest exponential divisor (A322791) of n that is cubefree (A004709). - Amiram Eldar, Jun 03 2025
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Brahim Mittou, New properties of an arithmetic function, Mathematica Montisnigri, Vol LIII (2022), pp. 5-11.
Eric Weisstein's World of Mathematics, Cubefree.
FORMULA
Multiplicative with a(p^e) = p^(2 - e mod 2), p prime, e>0.
Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/30) * Product_{p prime} (1 + 1/p^2 - 1/p^3) = 0.4296463408... . - Amiram Eldar, Oct 28 2022
MATHEMATICA
fx[{a_, b_}]:={a, If[EvenQ[b], 2, 1]}; Table[Times@@(#[[1]]^#[[2]]&/@(fx/@ FactorInteger[n])), {n, 70}] (* Harvey P. Dale, Jan 01 2012 *)
PROG
(Haskell)
a066990 n = product $ zipWith (^)
(a027748_row n) (map ((2 -) . (`mod` 2)) $ a124010_row n)
-- Reinhard Zumkeller, Dec 02 2012
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(2 - f[i, 2]%2)); } \\ Amiram Eldar, Oct 28 2022
(Python)
from math import prod
from sympy import factorint
def a(n): return prod(p**(2-(e&1)) for p, e in factorint(n).items())
print([a(n) for n in range(1, 70)]) # Michael S. Branicky, Jun 03 2025
CROSSREFS
KEYWORD
nonn,nice,mult,easy
AUTHOR
Reinhard Zumkeller, Feb 01 2002
STATUS
approved
