A066946 Numbers n such that phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = sigma(n).

827, 975, 1607, 13149, 20919, 34921, 58649, 202223, 347869, 545377, 900521, 1451135, 2288845, 2453509, 2804855, 3063031, 4134579, 11320177, 11446955, 14573651, 16477307, 17678225, 25164429, 27514643, 28475077, 47443799, 49348333, 50971501, 53108173, 66213757

Offset

1,1

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..54

Example

Let n = 827. Then phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(826) + sigma(828) - phi(828) - sigma(826) = 348 + 2184 - 264 - 1440 = 828 = sigma(n), so 827 is in the sequence.

Mathematica

g[x_] := Module[{a, b, c, d, e, f}, a=EulerPhi[x]; b=DivisorSigma[1, x]; c=EulerPhi[a]; d=DivisorSigma[1, b]; e=EulerPhi[b]; f=DivisorSigma[1, a]; c+d-e-f==b]; Do[If[g[n]==True, Print[n]], {n, 1, 10^5}]

Crossrefs

Cf. A000010, A000203, A066850, A066939, A066945.

Sequence in context: A251616 A251611 A104375 * A143799 A046496 A102350

Adjacent sequences: A066943 A066944 A066945 * A066947 A066948 A066949

Keyword

nonn

Author

Joseph L. Pe, Jan 24 2002

Extensions

Edited by Dean Hickerson and Robert G. Wilson v, Jan 26 2002

a(23)-a(26) from Donovan Johnson, Jan 02 2009

a(27)-a(30) from Hiroaki Yamanouchi, Sep 20 2014

Status

approved