A046027 Smallest multiple prime factor of the n-th nonsquarefree number (A013929).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Crossrefs

Cf. A013929, A020639, A046028, A249739.

Sequence in context: A141242 A130451 A130285 * A283671 A046028 A330406

Adjacent sequences: A046024 A046025 A046026 * A046028 A046029 A046030

Keyword

nonn

Author

Eric W. Weisstein

Status

approved