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Search: id:A066175
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| A066175 |
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Numbers n such that sigma(phi(sigma(n))) = n. |
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+0
2
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| 1, 3, 7, 15, 31, 127, 1023, 8191, 131071, 524287, 2147483647
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If n=2^k-1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k-1), then n is in the sequence; are there any terms not of these forms? The last form includes the terms 15 and 1023; are there others like this?
Is this sequence infinite?
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EXAMPLE
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sigma(phi(sigma(31))) = sigma(phi(32)) = sigma(16) = 31.
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MATHEMATICA
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Select[Range[1, 10^6], DivisorSigma[1, EulerPhi[DivisorSigma[1, # ]]]==#&]
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CROSSREFS
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Adjacent sequences: A066172 A066173 A066174 this_sequence A066176 A066177 A066178
Sequence in context: A057613 A129984 A024876 this_sequence A132978 A117079 A026745
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KEYWORD
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nonn,more
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 15 2001
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Feb 20 2002
a(11) from Jud McCranie, Jun 23, 2005. No more terms < 4000000000.
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