A137924 - OEIS

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A137924

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

4, 3, 8, 9, 2, 1, 2, 15, 16, 9, 20, 7, 22, 3, 1, 13, 27, 7, 30, 1, 11, 17, 35, 1, 38, 3, 40, 3, 44, 1, 46, 3, 49, 25, 51, 13, 54, 55, 56, 57, 58, 5, 62, 63, 64, 65, 66, 17, 69, 7, 8, 37, 75, 19, 7, 39, 80, 81, 82, 7, 85, 43, 29, 11, 18, 91, 92, 93, 94, 19, 96, 49, 99, 25, 34, 13, 15, 53

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

OFFSET

1,1

COMMENTS

a(n) = A002808(n) for n in A073258. - Robert Israel, Dec 20 2023

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The 12th composite is 21. The divisors of 21 are 1,3,7,21. The divisors of 21 that are coprime to 12 are 1 and 7. 7 is the largest of these; so a(12) = 7.

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: A137924 := proc(n) local dvs, d ; dvs := sort(convert(numtheory[divisors](A002808(n)), list), `>`) ; for d in dvs do if gcd(d, n) = 1 then RETURN(d) ; fi ; od: end: seq(A137924(n), n=1..80) ; # R. J. Mathar, Mar 03 2008

MATHEMATICA

a = {}; c = 4; For[n = 1, n < 80, n++, AppendTo[a, Select[Divisors[c], GCD[ #, n] == 1 &][[ -1]]]; If[PrimeQ[c + 1], c = c + 2, c = c + 1]]; a (* Stefan Steinerberger, Mar 09 2008 *)

CROSSREFS

Cf. A002808, A073258, A137925.

Sequence in context: A131416 A134390 A004125 * A171527 A240969 A198576

Adjacent sequences: A137921 A137922 A137923 * A137925 A137926 A137927

KEYWORD

nonn,look

AUTHOR

Leroy Quet, Feb 23 2008

EXTENSIONS

More terms from R. J. Mathar and Stefan Steinerberger, Mar 03 2008

STATUS

approved