A162022 Smallest prime factor of n-th odd composite integers A071904.

3, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 5, 3, 3, 5, 3, 3, 7, 3, 5, 3, 7, 3, 5, 3, 3, 3, 5, 3, 7, 11, 3, 5, 3, 7, 3, 3, 11, 5, 3, 3, 5, 3, 7, 3, 13, 3, 5, 3, 3, 5, 11, 3, 3, 3, 7, 5, 3, 11, 3, 5, 7, 3, 13, 3, 3, 5, 3, 3, 5, 13, 3, 11, 3, 7, 3, 5, 3, 3, 5, 3, 3, 7, 17, 3, 5, 3, 13, 7, 3, 5, 3, 3, 11, 3, 17, 5, 3, 7, 3

Offset: 1

Author

Zak Seidov, Jun 25 2009

Keywords

• nonn

Comments

Records are for n's such that A071904(n) = squares of primes.

a(n) = A020639(A071904(n)). [Reinhard Zumkeller, Oct 10 2011]

Examples

			A071904(1)=9, hence a(1)=3, A071904(4)=25, hence a(4)=5.
		

Links

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

Crossrefs

Cf. A014076, A071904.

Programs

Mathematica

nn=501;With[{ci=Complement[Range[9,nn,2],Prime[Range[PrimePi[nn]]]]}, FactorInteger[ #][[1,1]]&/@ci] (* Harvey P. Dale, Nov 30 2012 *)

Python

from sympy import primepi, primefactors
def A162022(n):
    if n == 1: return 3
    m, k = n, primepi(n) + n + (n>>1)
    while m != k:
        m, k = k, primepi(k) + n + (k>>1)
    return min(primefactors(m)) # Chai Wah Wu, Jul 31 2024

Extensions

Corrected example a(4)=5 Francesco Antoni (francesco_antoni(AT)yahoo.com), Aug 04 2010