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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, 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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 31 2008
EXTENSIONS
More terms from Robert G. Wilson v, Sep 08 2008
STATUS
approved