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A065557
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Solutions n of the equation phi(n) = phi(n-1) + phi(n-2).
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5
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3, 5, 7, 11, 17, 23, 37, 41, 47, 101, 137, 233, 257, 857, 1037, 1297, 1541, 1601, 2017, 4337, 6527, 9179, 14401, 16097, 30497, 55387, 61133, 62801, 65537, 72581, 77617, 110177, 152651, 179297, 244967, 299651, 603461, 619697, 686737, 1876727
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All terms listed here are squarefree. (Thanks to Vladeta Jovovic for this observation.) Prove or disprove: a(n) is always squarefree.
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover Pub., NY 1966.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,85
J. L. Pe, On Solutions of phi(n) = phi(n-1) + phi(n-2): A Problem Proposal
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EXAMPLE
| phi(23) = 22 = 10 + 12 = phi(22) + phi(21), phi(101) = 100 = 40 + 60 = phi(100) + phi(99).
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MATHEMATICA
| Select[ Range[3, 10^6], EulerPhi[ # ] == EulerPhi[ # - 1] + EulerPhi[ # - 2] & ]
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PROG
| (PARI): for(n=3, 10^8, if(eulerphi(n)==eulerphi(n-1)+eulerphi(n-2), print1(n, ", ")))
(PARI) { n=0; e1=eulerphi(2); e2=eulerphi(1); for (m=3, 10^9, e=eulerphi(m); if (e==e2 + e1, write("b065557.txt", n++, " ", m); if (n==100, return)); e2=e1; e1=e ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 22 2009]
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CROSSREFS
| Cf. A000010. A065572 gives nonprime solutions.
Sequence in context: A108539 A170886 A090919 * A152999 A024967 A135246
Adjacent sequences: A065554 A065555 A065556 * A065558 A065559 A065560
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Nov 28 2001
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EXTENSIONS
| More terms from Jason Earls (zevi_35711(AT)yahoo.com), Robert G. Wilson v (rgwv(AT)rgwv.com) and Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 30 2001
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