A056608 Least prime factor of the n-th composite number.

2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 7, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 7, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2, 2

Offset: 1

Author

Odimar Fabeny, Aug 07 2000

Keywords

• easy
• nonn

Comments

Record values are seen when n = A120389(m). Conjecture: at each new record the count of the prior record follows A247509. Records seen are 2, 3, 5, 7, 11, ... and when 3, 5, 7, 11 are first seen, there have been 3, 3, 2, and 4 occurrences of 2, 3, 5, and 7. These are A247509(1) through A247509(4). Thus, the count for prime(60) would be A247509(60). - Bill McEachen, Jun 17 2024

Links

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

Crossrefs

Cf. A052369 (largest prime factor of n, where n runs through composite numbers). - Klaus Brockhaus, Jun 23 2009

Cf. A160180.

Programs

Haskell

a056608 = a020639 . a002808  -- Reinhard Zumkeller, Mar 29 2014

Magma

[ PrimeDivisors(n)[1]: n in [2..140] | not IsPrime(n) ]; // Klaus Brockhaus, Jun 23 2009

Mathematica

DeleteCases[Table[FactorInteger[n][[1, 1]] * Boole[Not[PrimeQ[n]]], {n, 2, 100}], 0] (* Alonso del Arte, Aug 21 2014 *)
FactorInteger[#][[1,1]]&/@Select[Range[200],CompositeQ] (* Harvey P. Dale, Mar 16 2023 *)

PARI

forcomposite(n=1, 1e2, p=factor(n)[1, 1]; print1(p, ", ")) \\ Felix Fröhlich, Aug 03 2014

Python

from sympy import composite, factorint
def A056608(n):
    return min(factorint(composite(n))) # Chai Wah Wu, Jul 22 2019

Formula

a(n) = A020639(A002808(n)) = A000040(A118663(n)). - M. F. Hasler, Apr 03 2012

Extensions

More terms from James Sellers, Aug 25 2000

Definition corrected by Reinhard Zumkeller, Mar 29 2014

Name changed by Alonso del Arte, Aug 21 2014