A073258 -id:A073258 - cp's OEIS frontend

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

Offset: 1

Leroy Quet, Feb 23 2008

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

			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.

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

Cf. A002808, A073258, A137925.

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

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 *)

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

A073257 Smallest k such that gcd(c(k),k) = gcd(A002808(k),k) = A064814(k) = n.

Original entry on oeis.org

1, 2, 12, 20, 5, 6, 7, 64, 234, 50, 55, 24, 26, 28, 30, 32, 629, 1008, 209, 220, 231, 1012, 506, 168, 425, 182, 189, 2716, 2204, 1080, 93, 96, 99, 2176, 105, 4428, 1369, 5586, 1755, 1800, 6109, 2478, 2279, 3916, 5760, 644, 4606, 1920, 1960, 10250, 2040, 2444

Offset: 1

Labos Elemer, Jul 22 2002

nonn

			50th composite is 70, gcd(50,70)=10 appears first here, a(10)=50.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A064814, A002808, A073258.

f[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] t=Table[0, {100}]; Do[s=GCD[f[n], n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t

a(n) = min{x: gcd(c(x), x)=n}, where c(x) is the x-th composite number.

A334880 Numbers k such that gcd(k, k-th composite number) > 1.

Original entry on oeis.org

2, 5, 6, 7, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32, 34, 36, 42, 48, 50, 51, 52, 54, 55, 56, 60, 62, 63, 64, 65, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 93, 96, 98, 99, 102, 104, 105, 110, 112, 114, 120, 122, 124, 126, 128, 130, 132, 138, 148

Offset: 1

Clark Kimberling, Jul 17 2020

			In the following table, c(k) = A002808(k) = k-th composite number.
  k     c(k)   gcd(k, c(k))
  1      4         1
  2      6         2
  3      8         1
  4      9         1
  5     10         5
  6     12         6
2, 5, 6 are in this sequence, and 1,3,4 are in A073258.

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

Cf. A002808, A064814, A073258 (complement), A336323.

c = Select[Range[2, 150], ! PrimeQ[#] &]; (* A002808 *)
Select[Range[Length[c]], GCD[c[[#]], #] > 1 &]  (* A334880 *)
Module[{nn=200,cmps,len},cmps=Select[Range[nn],CompositeQ];len=Length[ cmps];Select[Thread[{Range[len],cmps}],GCD@@#>1&]][[All,1]] (* Harvey P. Dale, Sep 20 2020 *)

lista(nn) = {my(n=0, list=List()); forcomposite (c=1, nn, n++; if (gcd(n, c) > 1, listput(list, n))); Vec(list);} \\ Michel Marcus, Jul 19 2020

cp's OEIS Frontend

A137924 a(n) = the largest divisor of A002808(n) that is coprime to n. (A002808(n) = the n-th composite.)

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A073257 Smallest k such that gcd(c(k),k) = gcd(A002808(k),k) = A064814(k) = n.

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A334880 Numbers k such that gcd(k, k-th composite number) > 1.

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