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A066850 Numbers n such that phi(phi(n)) + sigma(sigma(n)) = phi(sigma(n)) + sigma(phi(n)), where phi=A000010 is Euler's totient function and sigma=A000203 is the sum of divisors function. 4
1, 4, 2669, 9559, 15293, 32583, 36593, 38443, 255367, 257239, 273977, 283391, 314101, 421553, 488363, 532975, 768699, 839973, 871757, 1960479, 2337221, 2374867, 3084659, 3326653, 3735029, 4440017, 5387373, 7930439, 8114377 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..114

EXAMPLE

Let n = 2669. Then phi(phi(n)) + sigma(sigma(n)) = phi(2496) + sigma(2844) = 768 + 7280 = 8048 and phi(sigma(n)) + sigma(phi(n)) = phi(2844) + sigma(2496) = 936 + 7112 = 8048. So 2669 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]; Do[If[g[n] == 0, Print[n]], {n, 1, 10^6}]

PROG

(PARI) { n=0; for (m=1, 10^10, e=eulerphi(m); s=sigma(m); if (eulerphi(e) + sigma(s) == eulerphi(s) + sigma(e), write("b066850.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Apr 02 2010

CROSSREFS

Sequence in context: A280790 A079187 A131587 * A066837 A275683 A297008

Adjacent sequences:  A066847 A066848 A066849 * A066851 A066852 A066853

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Jan 24 2002

EXTENSIONS

Edited by Dean Hickerson, Jan 24 2002

STATUS

approved

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Last modified April 16 09:36 EDT 2021. Contains 343030 sequences. (Running on oeis4.)