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A093034
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Primes of the form 1+multiple perfect numbers.
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6
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2, 7, 29, 673, 30241, 523777, 2178541, 23569921, 33550337, 66433720321, 137438691329, 30823866178561, 796928461056001, 1802582780370364661761, 9186050031556349952001, 2827987212986831882236723201
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OFFSET
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1,1
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COMMENTS
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Theorem: If p is a term of this sequence and p-1 is a t-perfect number then for each positive integer k, x=p^k is a solution to the equation sigma(phi(x)) = t*(x-1).
Proof: sigma(phi(x))=sigma(phi(p^k))=sigma((p-1)*p^(k-1))=sigma(p-1)*sigma(p^(k-1))=t*(p-1)*(p^k-1)/(p-1)=t*(p^k-1)=t*(x-1). (End)
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LINKS
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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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