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A279731
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Composite numbers k such that the sum of the proper divisors of k is a power of 2.
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1
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9, 10, 12, 26, 49, 56, 58, 76, 122, 332, 568, 961, 992, 1018, 2042, 3344, 4336, 8186, 16129, 16256, 32762, 37432, 82704, 227744, 266176, 269072, 299576, 856544, 2097146, 5385812, 8388602, 9834772, 16580864, 17895664, 19173944, 33554426, 34636768, 61008020, 67092481, 67100672
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OFFSET
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1,1
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COMMENTS
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If m = 2^j-1 is a Mersenne prime then m^2 and m*(2^j) (twice a perfect number) are terms. If m-2 is also a prime, then 2*(m-2) is a term. - Metin Sariyar, Mar 31 2020
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LINKS
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EXAMPLE
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12 is a term because 1 + 2 + 3 + 4 + 6 = 2^4.
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MATHEMATICA
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Select[Range[7*10^7], CompositeQ[#]&&IntegerQ[Log[2, Total[ Most[ Divisors[ #]]]]]&] (* Harvey P. Dale, Apr 01 2018 *)
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PROG
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(PARI) isok(n) = ispower(sigma(n)-n, , &k) && (k==2); \\ Michel Marcus, Dec 18 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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STATUS
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approved
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