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A110075
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Numbers of the form 3*2^p*(2^p-1) where 2^p-1 is a (Mersenne) prime greater than 3.
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1
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168, 2976, 48768, 201302016, 51539214336, 824632147968, 13835058048839712768, 15950735949418990467928155695723053056, 1149371655649416643768760268505821828785983929289015296
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If n is in the sequence then sigma(n) = 4*(n-phi(n)) because phi(n) = phi(3)*phi(2^p)*phi(2^p-1) = 2^p*(2^p-2) hence 4*(n-phi(n)) = 4*(3*2^p*(2^p-1)-2^p*(2^p-2)) = 4*2^p* (3*2^p-3-2^p+2) = 4*2^p*(2^(p+1)-1) = sigma(3)*sigma(2^p-1)* sigma(2^p) = sigma(3*(2^p-1)*2^p) = sigma(n). So this sequence is a subsequence of A068420.
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MATHEMATICA
| Do[If[PrimeQ[2^Prime[n] - 1], Print[3*2^Prime[n]* (2^Prime[n] - 1)]], {n, 2, 28}]
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CROSSREFS
| Cf. A000668, A068420.
Sequence in context: A110285 A070835 A112551 * A003807 A011785 A003800
Adjacent sequences: A110072 A110073 A110074 * A110076 A110077 A110078
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KEYWORD
| nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 27 2005; definition corrected Apr 22 2006
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