A160180 Largest proper divisor of the n-th composite number.

2, 3, 4, 3, 5, 6, 7, 5, 8, 9, 10, 7, 11, 12, 5, 13, 9, 14, 15, 16, 11, 17, 7, 18, 19, 13, 20, 21, 22, 15, 23, 24, 7, 25, 17, 26, 27, 11, 28, 19, 29, 30, 31, 21, 32, 13, 33, 34, 23, 35, 36, 37, 25, 38, 11, 39, 40, 27, 41, 42, 17, 43, 29, 44, 45, 13, 46, 31, 47, 19, 48, 49, 33, 50, 51, 52

Offset: 1

Author

Kyle Stern, May 03 2009, May 04 2009

Keywords

• easy
• nonn

Comments

Old name: The n-th positive composite number divided by its lowest nontrivial factor.

Examples

			a(1) = 4/2 = 2, a(2) = 6/2 = 3, a(3) = 8/2 = 4, a(4) = 9/3 = 3, a(5) = 10/2 = 5.
		

Links

• K. Stern, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A002808, A032742, A056608, A163870, A144925.

Programs

Haskell

a160180 = a032742 . a002808  -- Reinhard Zumkeller, Mar 29 2014

MATLAB

function [a] = A160180(k) j = 0; n = 1; while j < k if isprime(n) == 1 skip elseif isprime(n) == 0 j = j + 1; factors = factor(n); lowfactor = factors(1,1); a(j,1) = n/lowfactor; end n = n + 1; end - Kyle Stern, May 04 2009

Mathematica

f[n_] := Block[{k = n + PrimePi@ n + 1}, While[k != n + PrimePi@ k + 1, k++ ]; k/FactorInteger[k][[1, 1]]]; Array[f, 75] (* Robert G. Wilson v, May 11 2012 *)
Divisors[#][[-2]]&/@Select[Range[200],CompositeQ] (* Harvey P. Dale, Dec 06 2021 *)
(# / FactorInteger[#][[1, 1]])& /@ Select[Range[300], CompositeQ] (* Amiram Eldar, Jun 18 2022 *)

Formula

a(n) = A032742(A002808(n)) = A002808(n) / A056608(n) = A163870(n,A144925(n)). - Reinhard Zumkeller, Mar 29 2014

Extensions

Indices of b-file corrected, more terms added using b-file. - N. J. A. Sloane, Aug 31 2009

New name from Reinhard Zumkeller, Mar 29 2014

Incorrect formula removed by Ridouane Oudra, Oct 15 2021