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A181711
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Numbers of the form m*(2^k-1), where m = 2^(k-1)*(2^k-1) is a perfect number (A000396).
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0
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OFFSET
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1,1
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COMMENTS
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The associated exponents k are in A000043: 2, 3, 5, 7, 13, 17, 19 ,31, 61, ...
One can prove that, if m = 2^(k-1)*(2^k-1) is a perfect number, then m*2^k and m*(2^k-1) are both in A181595. Thus every even term in A000396 is a difference of two terms in A181595.
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LINKS
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FORMULA
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If odd perfect numbers do not exist, then a(n) = A181710(n) - A000396(n).
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EXAMPLE
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With k=3, m = 2^(k-1)*(2^k - 1) = 2^2*(8 - 1) = 28 is a perfect number (A000396), so m*(2^k - 1) = 28*7 = 196 is in the sequence. - Michael B. Porter, Jul 19 2016
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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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