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

1,1

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

Formula

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

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 *)

Prog

(Magma) [ PrimeDivisors(n)[1]: n in [2..140] | not IsPrime(n) ]; // Klaus Brockhaus, Jun 23 2009
(Haskell)
a056608 = a020639 . a002808  -- Reinhard Zumkeller, Mar 29 2014
(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

Crossrefs

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

Cf. A160180.

Sequence in context: A306249 A064656 A270776 * A091787 A087040 A065569

Adjacent sequences: A056605 A056606 A056607 * A056609 A056610 A056611

Keyword

easy,nonn

Author

Odimar Fabeny, Aug 07 2000

Extensions

More terms from James A. Sellers, Aug 25 2000

Definition corrected by Reinhard Zumkeller, Mar 29 2014

Name changed by Alonso del Arte, Aug 21 2014

Status

approved