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Search: id:A066228
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| A066228 |
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The EulerPhi(sigma(EulerPhi))-perfect numbers, where the f-perfect numbers for an arithmetical function f are defined in A066218. |
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+0
1
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OFFSET
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1,1
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COMMENT
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There are no terms between 449 and 10^5. Are there any more terms? Are there infinitely many?
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LINKS
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J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.
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EXAMPLE
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Let f(n) = EulerPhi(sigma(EulerPhi(n)). Proper divisors of 28 = {1, 2, 4, 7, 14}; the sum of their f-values = 1+1+2+4+4 = 12 = f(28); hence 28 belongs to the sequence.
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MATHEMATICA
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f[x_] := EulerPhi[DivisorSigma[1, EulerPhi[x]]]; Select[ Range[ 1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]
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CROSSREFS
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Sequence in context: A104465 A098515 A059719 this_sequence A110881 A156449 A117443
Adjacent sequences: A066225 A066226 A066227 this_sequence A066229 A066230 A066231
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 18 2001
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