A143772 If m is the n-th composite, then a(n) = gcd(k + m/k), where k is over all divisors of m.

1, 1, 3, 2, 1, 1, 3, 8, 1, 1, 3, 2, 1, 1, 2, 3, 4, 1, 1, 3, 2, 1, 12, 1, 3, 8, 1, 1, 3, 2, 1, 1, 2, 3, 4, 1, 1, 8, 3, 2, 1, 1, 3, 8, 1, 6, 1, 3, 2, 1, 1, 3, 4, 1, 6, 1, 3, 2, 1, 1, 2, 3, 8, 1, 1, 4, 3, 2, 1, 24, 1, 3, 4, 1, 1, 3, 2, 1, 1, 3, 8, 1, 1, 4, 3, 2, 1, 24, 1, 2, 3, 4, 1, 6, 1, 3, 2, 1, 1, 2, 3, 8, 1, 1, 3

Offset: 1

Author

Leroy Quet, Aug 31 2008

Keywords

• nonn

Comments

Conjecture: All even numbers are terms and the only odd numbers which are terms are 1 and 3. - Robert G. Wilson v, Sep 08 2008

Examples

			For n=11, 20 is the 11th composite. So we have a(11) = gcd(1+20, 2+10, 4+5, 5+4, 10+2, 20+1) = 3.
		

Crossrefs

Cf. A143771.

Programs

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; f[n_] := Block[{m = Composite@n}, Last@ FoldList[ GCD, m!, # + m/# & /@ Divisors@m]]; Array[f, 105] (* Robert G. Wilson v, Sep 08 2008 *)

Extensions

More terms from Robert G. Wilson v, Sep 08 2008