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

1,3

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

Links

Table of n, a(n) for n=1..105.

Example

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.

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 *)

Crossrefs

Cf. A143771.

Sequence in context: A134520 A188316 A197027 * A373366 A373377 A053989

Adjacent sequences: A143769 A143770 A143771 * A143773 A143774 A143775

Keyword

nonn

Author

Leroy Quet, Aug 31 2008

Extensions

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

Status

approved