A073813 Difference between n and largest unrelated number belonging to n, when n runs over composite numbers. For primes and for 4, unrelated set is empty.

0, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 7, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 7, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2

Offset: 1

Author

Labos Elemer, Aug 15 2002

Keywords

• nonn

Comments

From Michael De Vlieger, Mar 28 2016 (Start):

a(0) = 0 since 4 is the smallest composite and "unrelated" numbers k with respect to n must be composite and smaller than n. Unrelated numbers k cannot be prime since primes p must either divide or be coprime to n; k cannot equal 1 since 1 is both a divisor of and coprime to n.

The test for unrelated numbers k that belong to n is 1 < gcd(k, n) < k.

(End)

Examples

			composite[1]=4, URS[4]={}, a(1)=0 by convention; n=14, c[14]=24, URS[24]={9,10,14,15,16,18,20,21,22}, a(14)=24-Max[URS[24]]=2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045763, A073759, A002808.

Cf. A056608. [From R. J. Mathar, Sep 23 2008]

Programs

Mathematica

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x]; tn[x_] := Table[j, {j, 1, x}]; di[x_] := Divisors[x]; rrs[x_] := Flatten[Position[GCD[tn[x], x], 1]]; rs[x_] := Union[rrs[x], di[x]]; urs[x_] := Complement[tn[x], rs[x]]; Table[c[w]-Max[urs[c[w]]], {w, 1, 128}]
Prepend[Function[k, k - SelectFirst[Range[k - 2, 2, -1], 1 < GCD[#, k] < # &]] /@ Select[Range[6, 138], ! PrimeQ@ # &], 0] (* Michael De Vlieger, Mar 28 2016, Version 10 *)

Formula

See program.