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Search: id:A104902
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| A104902 |
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Numbers n such that sigma(n)=12*phi(n). |
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+0
4
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| 210, 1848, 2970, 3720, 6270, 26796, 38340, 53940, 59340, 60960, 70686, 78210, 80940, 88536, 129540, 142290, 149226, 155064, 174174, 237000, 249210, 300390, 350610, 385710, 429408, 526110, 604128, 624840, 664608, 827310, 828072, 842010
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OFFSET
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1,1
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COMMENT
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If p>2 and 2^p-1 is prime (Merssene prime) then 15*2^(p-2)*(2^p-1) is in the sequence. So 15*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence.
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EXAMPLE
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p>2, q=2^p-1(q is prime); m=15*2^(p-2)*q so sigma(m)=24*(2^(p-1)-1)*2^p
=12*(8*2^(p-3)*(2^p-2))=12*phi(m) hence m is in the sequence.
sigma(237000)=748800=12*62400=12*phi(237000) so 237000 is in
the sequence but 237000 isn't of the form 15*2^(p-2)*(2^p-1).
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MATHEMATICA
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Do[If[DivisorSigma[1, m] == 12*EulerPhi[m], Print[m]], {m, 1200000}]
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CROSSREFS
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Cf. A000043, A062699, A068390, A104900, A104901.
Sequence in context: A046302 A118281 A047633 this_sequence A135201 A064260 A027806
Adjacent sequences: A104899 A104900 A104901 this_sequence A104903 A104904 A104905
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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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