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Search: id:A066226
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| A066226 |
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The sigma(EulerPhi)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is 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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These are all the terms less than 10^5. Problem: Find an expression generating all the terms.
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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) = sigma(EulerPhi(n)). The proper divisors of 88 are {1, 2, 4, 8, 11, 22, 44}; adding their f-values: 1 + 1 + 3 + 7 + 18 + 18 + 42 = 90 = f(88). Hence 88 is a term of the sequence.
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MATHEMATICA
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f[x_] := 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: A101578 A041881 A076542 this_sequence A058439 A058463 A166848
Adjacent sequences: A066223 A066224 A066225 this_sequence A066227 A066228 A066229
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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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