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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A324533 A377671 A141128 * A319351 A323373 A332826

Adjacent sequences: A160177 A160178 A160179 * A160181 A160182 A160183

Keyword

easy,nonn

Author

Kyle Stern, May 03 2009, May 04 2009

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

Status

approved