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A078148
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Numbers n such that d[phi(n)]-phi[d(n)]=0, where d()=A000005(), phi()=A000010().
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2
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1, 2, 4, 6, 16, 24, 30, 36, 64, 384, 408, 480, 510, 1024, 1296, 1560, 1680, 2304, 2640, 3480, 4096, 5440, 5520, 6360, 9240, 11280, 14040, 14160, 14400, 15120, 15960, 17880, 19320, 19920, 20760, 22848, 24480, 25680, 26880, 30360, 32280, 35160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 2^m is in the sequence iff m=0 or m+1 is prime (the proof is easy). Also all numbers of the form 3*2^(2^m-1) are in the sequence because d(phi(3*2^(2^m-1)))-phi(d(3*2^(2^m-1)))=d(2*2^(2^m-2))- phi(2*2^m)=d(2^(2^m-1))-phi(2^(m+1))=2^m-2^m=0. So this sequence is infinite. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 25 2006
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..500
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EXAMPLE
| n=24:d[24]=8,phi[8]=4,phi[24]=8,d[8]=4, so 24 is here.
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MATHEMATICA
| cm[x_] := DivisorSigma[0, EulerPhi[x]]-EulerPhi[DivisorSigma[0, x]] Do[s=cm[n]; If[Equal[s, 0], Print[n]], {n, 1, 100000}]
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CROSSREFS
| Cf. A000005, A000010.
Cf. A033632
Sequence in context: A067662 A001774 A053285 * A076075 A030157 A162580
Adjacent sequences: A078145 A078146 A078147 * A078149 A078150 A078151
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KEYWORD
| easy,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 26 2002
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