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

1,1

Comments

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

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A014076, A071904.

Sequence in context: A002373 A236569 A103153 * A318240 A262289 A096918

Adjacent sequences: A162019 A162020 A162021 * A162023 A162024 A162025

Keyword

nonn

Author

Zak Seidov, Jun 25 2009

Extensions

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

Status

approved