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A093034 Primes of the form 1+multiple perfect numbers. 5
2, 7, 29, 673, 30241, 523777, 2178541, 23569921, 33550337, 66433720321, 137438691329, 30823866178561, 796928461056001, 1802582780370364661761, 9186050031556349952001, 2827987212986831882236723201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From M. F. Hasler and Farideh Firoozbakht, Apr 08 2010: (Start)

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)

LINKS

Table of n, a(n) for n=1..16.

CROSSREFS

Cf. A007691.

Cf. A171263, A171264, A171265. [From M. F. Hasler and Farideh Firoozbakht, Apr 08 2010]

Sequence in context: A192410 A270518 A094475 * A125174 A270526 A037417

Adjacent sequences:  A093031 A093032 A093033 * A093035 A093036 A093037

KEYWORD

nonn

AUTHOR

Labos Elemer, May 12 2004

EXTENSIONS

a(11)-a(16) from Donovan Johnson, Nov 30 2008

STATUS

approved

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Last modified April 22 14:29 EDT 2019. Contains 322356 sequences. (Running on oeis4.)