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A046028
Largest multiple prime factor of the n-th nonsquarefree number (A013929).
4
2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, 2, 2, 3, 2, 7, 5, 2, 3, 2, 2, 3, 2, 2, 3, 5, 2, 2, 3, 2, 2, 3, 2, 2, 7, 3, 5, 2, 3, 2, 2, 3, 2, 11, 2, 5, 3, 2, 2, 3, 2, 2, 3, 7, 2, 5, 2, 3, 2, 2, 3, 2, 2, 13, 3, 2, 5, 2, 3, 2, 2, 3, 2, 7, 3, 5, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 3, 2, 2, 11, 3, 2, 7, 2, 5, 3, 2, 2, 3
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Greatest Prime Factor.
Eric Weisstein's World of Mathematics, Squareful.
FORMULA
a(n) = A249740(A013929(n)). - Amiram Eldar, Feb 11 2021
MATHEMATICA
Select[ FactorInteger[#]//Reverse, #[[2]]>1&, 1][[1, 1]]& /@ Select[ Range[300], !SquareFreeQ[#]& ] (* Jean-François Alcover, Nov 06 2012 *)
PROG
(Haskell)
a046028 n = a046028_list !! (n-1)
a046028_list = f 1 where
f x | null zs = f (x + 1)
| otherwise = (fst $ head zs) : f (x + 1)
where zs = reverse $ filter ((> 1) . snd) $
zip (a027748_row x) (a124010_row x)
-- Reinhard Zumkeller, Dec 29 2012
(Python)
from math import isqrt
from sympy import mobius, factorint
def A046028(n):
def f(x): return n+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
s = factorint(m)
return next(p for p in sorted(s, reverse=True) if s[p]>1) # Chai Wah Wu, Jul 22 2024
CROSSREFS
KEYWORD
nonn,easy,nice
STATUS
approved