A070815 Solutions to phi(gpf(x)) - gpf(phi(x)) = 254 = c are special multiples of 257, x = 257k, where largest prime factors of factor k were observed from {2, 3, 5, 17}. See solutions to other even cases of c (=A070813): A007283 for 0, A070004 for 2, A070814 for 14, A070816 for 65534.

257, 514, 771, 1028, 1285, 1542, 2056, 2570, 3084, 3855, 4112, 4369, 5140, 6168, 7710, 8224, 8738, 10280, 12336, 13107, 15420, 16448, 17476, 20560, 21845, 24672, 26214, 30840, 32896, 34952, 41120, 43690, 49344, 52428, 61680, 65535, 65792

Offset: 1

Author

Labos Elemer, May 09 2002

Keywords

• nonn

Examples

			For n = 87380 = 4*5*17*257, gpf(n) = 257, phi(n) = 65536, commutator[87380] = phi(257) - gpf(65536) = 256 - 2 = 254.
		

Crossrefs

Cf. A000010, A000215, A006530, A007283, A070002, A070002, A070004, A070777, A070812, A070813.

Programs

Mathematica

pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 254], Print[{n, n/257, pf[n/257]}]], {n, 3, 1000000}] (* Terms of sequence are n *)