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Search: id:A018784
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| A018784 |
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Numbers n such that sigma(phi(n)) = n. |
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+0
6
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| 1, 3, 15, 28, 255, 744, 2418, 20440, 65535, 548856, 2835756, 4059264, 4451832, 10890040, 13192608, 23001132, 54949482, 110771178, 220174080, 445701354, 4294967295, 16331433888, 18377794080, 94951936080, 204721968000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The numbers 2^2^n-1 for n=0,1,...,5 are in the sequence because 2^2^n-1=(2^2^0+1)*(2^2^1+1)*(2^2^2+1)*...*(2^2^(n-1)+1); 2^2^k+1 for k=0,1,2,3 & 4 are primes (Fermat primes); sigma(2^k)=2^(k+1)-1 and phi is a multiplicative function. Hence if p is a known Fermat prime (p=2^2^n+1 for n=0,1,2,3 & 4) then p-2 is in the sequence, note that this isn't true for unknown Fermat primes if they exist. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Aug 27 2004
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FORMULA
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sigma(A001229).
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CROSSREFS
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Cf. A097645, A097646, A019434.
Adjacent sequences: A018781 A018782 A018783 this_sequence A018785 A018786 A018787
Sequence in context: A077785 A015646 A067144 this_sequence A053519 A039666 A020493
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Wilson's search was complete only though a(19) = 50319360. Jud McCranie (j.mccranie(AT)comcast.net) reports Jun 15 1998 that the terms through a(24) are certain.
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