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A135241
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Numbers n such that sigma(sigma(n))=2*phi(n).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If p=2^n+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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EXAMPLE
| sigma(sigma(36300841))=sigma(36313684)=72576000=2*36288000=2*phi(36300841) so 36300841 is in the sequence.
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MATHEMATICA
| 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 (rgwv(AT)rgwv.com), Jan 01 2008
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CROSSREFS
| Sequence in context: A066465 A023262 A067260 * A104115 A063650 A144236
Adjacent sequences: A135238 A135239 A135240 * A135242 A135243 A135244
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KEYWORD
| nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 30 2007
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 01 2008
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