A073481 - OEIS

%I #30 Aug 29 2024 01:37:40

%S 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,

%T 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,

%U 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

%N Least prime factor of the n-th squarefree number.

%H Reinhard Zumkeller, <a href="/A073481/b073481.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A265668(n,1). - _Reinhard Zumkeller_, Dec 13 2015

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

%o (Haskell)

%o a073482 = a020639 . a005117  -- _Reinhard Zumkeller_, Feb 04 2012

%o (PARI) apply(x->(if (x==1,1, vecmin(factor(x)[,1]))), select(issquarefree, [1..150])) \\ _Michel Marcus_, Dec 17 2023

%o (Python)

%o from math import isqrt

%o from sympy import mobius, primefactors

%o def A073481(n):

%o     def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))

%o     kmin, kmax = 0,1

%o     while f(kmax) > kmax:

%o         kmax <<= 1

%o     while kmax-kmin > 1:

%o         kmid = kmax+kmin>>1

%o         if f(kmid) <= kmid:

%o             kmax = kmid

%o         else:

%o             kmin = kmid

%o     return min(primefactors(kmax),default=1) # _Chai Wah Wu_, Aug 28 2024

%Y Cf. A073482.

%Y Cf. A005117, A020639, A265668.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Aug 03 2002

%E More terms from _Jason Earls_, Aug 06 2002