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A160180 Largest proper divisor of the n-th composite number. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Old name: The n-th positive composite number divided by its lowest nontrivial factor.
LINKS
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
Sequence in context: A368695 A324533 A141128 * A319351 A323373 A332826
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

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Last modified April 16 17:08 EDT 2024. Contains 371749 sequences. (Running on oeis4.)