OFFSET
1,1
COMMENTS
For n > 10, a(n) = 2a(n-4). First, it is easy to show that with i >= 0 and k,m in {0,1}, a(n) are of the form 2^i*3^k*5^m. Factoring this sequence reveals the regular pattern 2^i, 2^(i-2)*5, 2^(i-1)*3, 2^(i-3)*3*5, 2^(i+1), ... which obviously has the property a(n) = 2a(n-4) for n > 10. - Lambert Herrgesell (lambert.herrgesell(AT)googlemail.com), Jan 09 2007
FORMULA
For n > 10, a(n) = 2a(n-4) (conjectured). - Ralf Stephan, May 09 2004
EXAMPLE
For n = 32640 = 128*3*5*17, gpf(n) = 17, phi(n) = 16384, commutator[32640] = phi(17) - gpf(16384) = 16 - 2 = 14.
MATHEMATICA
pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 14], Print[{n, n/17, pf[n/17]}]], {n, 3, 1000000}] (* Terms of sequence are n *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 09 2002
STATUS
approved