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Search: id:A070814
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| A070814 |
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Solutions to Phi[P[x]]-P[Phi[x]]=14=c are special multiples of 17, x=17k, where largest prime factors of factor k were observed from {2, 3, 5}, i.e. it is smaller than 17. See solutions to other even cases of c [=A070813]: A007283 for 0, A070004 for 2, A070815 for 254, A070816 for 65534. |
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| 17, 34, 51, 68, 85, 102, 136, 170, 204, 255, 272, 340, 408, 510, 544, 680, 816, 1020, 1088, 1360, 1632, 2040, 2176, 2720, 3264, 4080, 4352, 5440, 6528, 8160, 8704, 10880, 13056, 16320, 17408, 21760, 26112, 32640, 34816, 43520, 52224, 65280
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OFFSET
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1,1
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COMMENT
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For n>10, a(n) = 2a(n-4). First, it is easy to show that with i>=0 and k,m in {0,1}, a(n) are of the form 2^i*3^k*5^m. Factoring this sequence reveals the regular pattern 2^i, 2^(i-2)*5, 2^(i-1)*3, 2^(i-3)*3*5, 2^(i+1),... which obviously has the property a(n) = 2a(n-4) for n>10. - Lambert Herrgesell (lambert.herrgesell(AT)googlemail.com), Jan 09 2007
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FORMULA
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For n>10, a(n) = 2a(n-4) (conjectured). - R. Stephan, May 09 2004
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EXAMPLE
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n=32640=128.3.5.17, P[n]=17,Phi[n]=16384, commutator[32640]=Phi[17]-P[16384]=16-2=14
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MATHEMATICA
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pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 14], Print[{n, n/17, pf[n/17]}]], {n, 3, 1000000}] (*Terms of sequence are n*)
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CROSSREFS
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Cf. A000010, A006530, A070812, A070813, A000215, A070777, A070002-A070004, A007283.
Sequence in context: A033029 A044842 A033014 this_sequence A098365 A033899 A110287
Adjacent sequences: A070811 A070812 A070813 this_sequence A070815 A070816 A070817
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 09 2002
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