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Search: id:A104901
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| A104901 |
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Numbers n such that sigma(n)=8*phi(n). |
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+0
6
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| 42, 594, 744, 1254, 7668, 8680, 10788, 11868, 12192, 14630, 15642, 16188, 25908, 28458, 49842, 60078, 70122, 77142, 105222, 124968, 125860, 138460, 142240, 165462, 168402, 169608, 188860, 201924, 242316, 259160, 302260, 553000, 561906
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OFFSET
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1,1
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COMMENT
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If p>3 and 2^p-1 is prime (Merssene prime) then 35*2^(p-2)*(2^p-1) is in the sequence. So 35*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence.
If p>2 and 2^p-1 is prime (Merssene prime) then 3*2^(p-2)*(2^p-1) is in the sequence (the proof is easy). - Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 23 2007
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EXAMPLE
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p>3, q=2^p-1(q is prime); m=35*2^(p-2)*q so sigma(m)=48*(2^(p-1)-1)*2^p
=8*(24*2^(p-3)*(2^p-2))=8*phi(m) hence m is in the sequence.
sigm(553000)=1497600=8*187200=8*phi(553000) so 553000 is in the
sequence but 553000 isn't of the form 35*2^(p-2)*(2^p-1).
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MATHEMATICA
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Do[If[DivisorSigma[1, m] == 8*EulerPhi[m], Print[m]], {m, 1000000}]
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CROSSREFS
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Cf. A000043, A062699, A068390, A104900, A104902.
Sequence in context: A008387 A088626 A086944 this_sequence A091962 A007746 A030197
Adjacent sequences: A104898 A104899 A104900 this_sequence A104902 A104903 A104904
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KEYWORD
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easy,nonn
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AUTHOR
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Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Apr 01 2005
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