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

1,2

Links

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

Formula

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

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

Mathematica

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

Prog

(Haskell)
a073482 = a020639 . a005117  -- Reinhard Zumkeller, Feb 04 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

Crossrefs

Cf. A073482.

Cf. A005117, A020639, A265668.

Sequence in context: A359609 A272636 A066949 * A178094 A364874 A122556

Adjacent sequences: A073478 A073479 A073480 * A073482 A073483 A073484

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2002

Extensions

More terms from Jason Earls, Aug 06 2002

Status

approved