A073481 Least prime factor of the n-th squarefree number.

1, 2, 3, 5, 2, 7, 2, 11, 13, 2, 3, 17, 19, 3, 2, 23, 2, 29, 2, 31, 3, 2, 5, 37, 2, 3, 41, 2, 43, 2, 47, 3, 53, 5, 3, 2, 59, 61, 2, 5, 2, 67, 3, 2, 71, 73, 2, 7, 2, 79, 2, 83, 5, 2, 3, 89, 7, 3, 2, 5, 97, 101, 2, 103, 3, 2, 107, 109, 2, 3, 113, 2, 5, 2, 7, 2, 3, 127, 3, 2, 131, 7, 2, 137, 2, 139, 3, 2, 11, 5

Offset: 1

Author

Reinhard Zumkeller, Aug 03 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073482.

Cf. A005117, A020639, A265668.

Programs

Haskell

a073482 = a020639 . a005117  -- Reinhard Zumkeller, Feb 04 2012

Mathematica

a = Select[Range[300], SquareFreeQ[#]&]; Table[FactorInteger[a[[n]]][[1,1]], {n, Length[a]}] (* Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)

PARI

apply(x->(if (x==1,1, vecmin(factor(x)[,1]))), select(issquarefree, [1..150])) \\ Michel Marcus, Dec 17 2023

Python

from math import isqrt
from sympy import mobius, primefactors
def A073481(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    kmin, kmax = 0,1
    while f(kmax) > kmax:
        kmax <<= 1
    while kmax-kmin > 1:
        kmid = kmax+kmin>>1
        if f(kmid) <= kmid:
            kmax = kmid
        else:
            kmin = kmid
    return min(primefactors(kmax),default=1) # Chai Wah Wu, Aug 28 2024

Formula

a(n) = A020639(A005117(n)).

a(n) = A265668(n,1). - Reinhard Zumkeller, Dec 13 2015

Extensions

More terms from Jason Earls, Aug 06 2002