A137925 - OEIS

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A137925

a(n) = the largest divisor of n that is coprime to A002808(n). (A002808(n) = the n-th composite.)

1, 1, 3, 4, 1, 1, 1, 8, 9, 5, 11, 4, 13, 7, 3, 1, 17, 9, 19, 5, 7, 11, 23, 1, 25, 2, 27, 1, 29, 2, 31, 1, 33, 17, 35, 9, 37, 38, 39, 40, 41, 7, 43, 44, 45, 46, 47, 3, 49, 1, 17, 13, 53, 27, 5, 7, 57, 58, 59, 5, 61, 31, 7, 1, 13, 66, 67, 68, 69, 14, 71, 9, 73, 37, 25, 19, 11, 39, 79, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

The 12th composite is 21. The divisors of 12 are 1,2,3,4,6,12. The divisors of 12 that are coprime to 21 are 1,2,4. 4 is the largest of these, so a(12) = 4.

MAPLE

A002808 := proc(n) option remember ; local a; if n = 1 then 4; else for a from A002808(n-1)+1 do if not isprime(a) then RETURN(a) ; fi ; od: fi ; end: A137925 := proc(n) local dvs, d, a002808 ; a002808 := A002808(n) ; dvs := sort(convert(numtheory[divisors](n), list), `>`) ; for d in dvs do if gcd(d, a002808) = 1 then RETURN(d) ; fi ; od: end: seq(A137925(n), n=1..120) ; # R. J. Mathar, Apr 17 2008

MATHEMATICA

ldc[{n_, x_}]:=Module[{divs=Divisors[n]}, Max[Select[divs, CoprimeQ[ #, x]&]]]; Module[{nn=120, c, len}, c=Select[Range[nn], CompositeQ]; len=Length[c]; ldc/@Thread[{Range[len], c}]] (* Harvey P. Dale, May 24 2017 *)

CROSSREFS

Cf. A137924.

Sequence in context: A058022 A215202 A139344 * A171528 A299924 A131107

Adjacent sequences: A137922 A137923 A137924 * A137926 A137927 A137928

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 23 2008

EXTENSIONS

More terms from R. J. Mathar, Apr 17 2008

STATUS

approved