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

1,1

Links

Table of n, a(n) for n=1..37.

Example

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

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 *)

Crossrefs

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

Sequence in context: A301619 A340343 A158231 * A095321 A100633 A007765

Adjacent sequences: A070812 A070813 A070814 * A070816 A070817 A070818

Keyword

nonn

Author

Labos Elemer, May 09 2002

Status

approved