|
|
A259788
|
|
Greatest prime factor of phi(binomial(2*n,n)).
|
|
3
|
|
|
2, 2, 3, 3, 5, 5, 5, 5, 5, 3, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 7, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 83, 83, 83, 83, 83, 83, 89
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
Conjectures:
(1) 7 is a unique term which is not a Sophie Germain prime (A005384);
(2) A Sophie Germain prime p occurs p times if and only if p=2,3,5 and 11; otherwise, it occurs q-p times, where q is the next Sophie Germain prime > p;
(3) a(n) is the greatest prime factor of p-1 for primes p in the interval (n, 2*n).
All these conjectures follow from the following strengthening of the Bertrand postulate for n>=24: the interval (n, 2*n) contains a safe prime (A005385).
|
|
LINKS
|
|
|
MATHEMATICA
|
Map[First[Last[FactorInteger[EulerPhi[Binomial[2#, #]]]]]&, Range[2, 100]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|