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A135241
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Numbers k such that sigma(sigma(k)) = 2*phi(k).
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3
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13, 43, 109, 151, 883, 2143, 116581, 388537, 1711663, 2498227, 4004107, 5550331, 12641137, 13617361, 18591967, 20755393, 22998397, 26838523, 29308291, 34564351, 36300841, 44829073, 82368469, 149460841, 184988197, 238225003, 252757891, 340428853
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OFFSET
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1,1
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COMMENTS
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If p = 2^k + 3 and both numbers p & q = (1/2)*(p^2 - 3p - 2) are primes then q is in the sequence, because sigma(sigma(q)) = sigma(q+1) = sigma((1/2)*(p-3)*p) = sigma(2^(n-1)*p) = (2^n-1)*(p+1) = (p-4)*(p+1) = p^2 - 3p - 4 = 2q - 2 = 2*phi(q). 13, 43, 151 & 2143 are such terms corresponding to n = 2, 3, 4 & 6.
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LINKS
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EXAMPLE
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sigma(sigma(36300841)) = sigma(36313684) = 72576000 = 2*36288000 = 2*phi(36300841) so 36300841 is in the sequence.
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MATHEMATICA
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lst = {}; fQ[n_] := DivisorSigma[1, DivisorSigma[1, n]] == 2 EulerPhi@n; Do[ If[ fQ@n, AppendTo[lst, n]; Print@n], {n, 252000000}] (* Robert G. Wilson v, Jan 01 2008 *)
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PROG
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(PARI) is(n) = sigma(sigma(n))==2*eulerphi(n) \\ Felix Fröhlich, May 18 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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