A143772 - OEIS

%I #11 Aug 02 2019 22:59:24

%S 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,

%T 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,

%U 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

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

%C 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

%e 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.

%t 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 *)

%Y Cf. A143771.

%K nonn

%O 1,3

%A _Leroy Quet_, Aug 31 2008

%E More terms from _Robert G. Wilson v_, Sep 08 2008