

A160180


Largest proper divisor of the nth composite number.


5



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
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OFFSET

1,1


COMMENTS

Old name: The nth positive composite number divided by its lowest nontrivial factor.
a(n) = A032742(A002808(n)) = A002808(n) / A056608(n) = A163870(n,A144925(n)).  Reinhard Zumkeller, Mar 29 2014


LINKS

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


FORMULA

a(n)=n/denom((2^n2)/n)  Vladimir Kruchinin, Aug 17 2010


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 *)


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: A324345 A324533 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 bfile corrected, more terms added using bfile.  N. J. A. Sloane, Aug 31 2009
New name from Reinhard Zumkeller, Mar 29 2014


STATUS

approved



