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A335254
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Numbers k such that the abundance (A033880) of k is equal to the deficiency (A033879) of k+1.
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3
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OFFSET
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1,1
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COMMENTS
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Equivalently, k and k+1 have the same absolute value of abundance (or deficiency) with opposite signs.
Equivalently, s(k) + s(k+1) = k + (k+1), where s(k) is the sum of proper divisors of k (A001065).
If k is a 3-perfect number (A005820) and k+1 is a prime, then k is in the sequence. Of the 6 known 3-perfect numbers only 672 and 523776 have this property.
a(4) > 10^11, if it exists.
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LINKS
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EXAMPLE
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672 is a term since A033880(672) = sigma(672) - 2*672 = 2016 - 1344 = 672, and A033879(673) = 2*673 - sigma(673) = 1346 - 674 = 672.
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MATHEMATICA
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ab[n_] := DivisorSigma[1, n] - 2*n; Select[Range[6 * 10^5], ab[#] == -ab[# + 1] &]
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CROSSREFS
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KEYWORD
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nonn,hard,bref,more
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AUTHOR
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STATUS
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approved
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