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A066945
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Numbers n such that phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(n).
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3
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11, 11063, 11943, 38585, 39995, 43021, 63349, 67709, 967393, 1267511, 2020925, 2915307, 5805559, 6584747, 6659429, 8064017, 26260385, 27681847, 31886881, 41932769, 48922307, 61270145, 71429011, 89087903, 91364345, 191945623
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,39
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EXAMPLE
| Let n = 11. Then phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(10) + sigma(12) - phi(12) - sigma(10) = 4 + 28 - 4 - 18 = 10 = phi(n), so 11 is in the sequence.
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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==a]; Do[If[g[n]==True, Print[n]], {n, 1, 10^5}]
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PROG
| (PARI) { n=0; for (m=1, 10^10, e=eulerphi(m); s=sigma(m); if (eulerphi(e) + sigma(s) - eulerphi(s) - sigma(e) == e, write("b066945.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 11 2010]
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CROSSREFS
| Cf. A000010, A000203, A066850, A066939, A066946.
Sequence in context: A138713 A068223 A068224 * A113615 A034873 A075854
Adjacent sequences: A066942 A066943 A066944 * A066946 A066947 A066948
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 24 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 26 2002
a(17)-a(26) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 02 2009
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