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URL: https://oeis.org/A046027

⇱ A046027 - OEIS

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A046027
Smallest multiple prime factor of the n-th nonsquarefree number (A013929).
7
2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 2, 2, 2, 3, 2, 7, 5, 2, 3, 2, 2, 3, 2, 2, 2, 5, 2, 2, 3, 2, 2, 3, 2, 2, 7, 3, 2, 2, 2, 2, 2, 3, 2, 11, 2, 5, 3, 2, 2, 3, 2, 2, 2, 7, 2, 5, 2, 3, 2, 2, 3, 2, 2, 13, 3, 2, 5, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 11, 3, 2, 7, 2, 5, 2, 2, 2, 3
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Least Prime Factor.
Eric Weisstein's World of Mathematics, Squareful.
FORMULA
a(n) = A249739(A013929(n)). - Amiram Eldar, Feb 11 2021
MATHEMATICA
Select[ FactorInteger[#], #[[2]]>1&, 1][[1, 1]]& /@ Select[ Range[300], !SquareFreeQ[#]& ] (* Jean-François Alcover, Nov 06 2012 *)
PROG
(Python)
from math import isqrt
from sympy import mobius, factorint
def A046027(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) if s[p]>1) # Chai Wah Wu, Jul 22 2024
(PARI) lista(nn) = apply(x->factor(x)[1, 1], apply(x->x/core(x), select(x->!issquarefree(x), [1..nn]))); \\ Michel Marcus, Jun 24 2025
CROSSREFS
KEYWORD
nonn
STATUS
approved