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A070816
Solutions to phi(gpf(x)) - gpf(phi(x)) = 65534 = c are special multiples of 65537, x=65537*k, where the largest prime factors of factor k were observed in {2, 3, 5, 17, 257}.
5
65537, 131074, 196611, 262148, 327685, 393222, 524296, 655370, 786444, 983055, 1048592, 1114129, 1310740, 1572888, 1966110, 2097184, 2228258, 2621480, 3145776, 3342387, 3932220, 4194368, 4456516, 5242960, 5570645, 6291552
OFFSET
1,1
COMMENTS
See solutions to other even cases of c [=A070813]: A007283 for 0, A070004 for 2, A070814 for 14, A070815 for 254.
EXAMPLE
For n = 572662306 = 2*17*257*65537, gpf(n) = 65537, phi(n) = 268435456, commutator[572662306] = phi(65537) - gpf(268435456) = 65536 - 2 = 65534.
MATHEMATICA
pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 65534], Print[{n, n/65537, pf[n/65537]}]], {n, 3, 1000000}] (* Terms of sequence are n *)
KEYWORD
nonn
AUTHOR
Labos Elemer, May 09 2002
STATUS
approved