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A125640
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Primitive doubly abundant numbers - doubly abundant numbers that are not the multiple of another doubly abundant number.
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2
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24, 30, 42, 54, 66, 78, 102, 114, 138, 140, 174, 176, 186, 222, 224, 246, 258, 282, 308, 318, 340, 354, 364, 366, 380, 402, 426, 438, 440, 474, 476, 498, 520, 532, 534, 580, 582, 606, 618, 642, 644, 654, 678, 762, 786, 812, 822, 834, 868, 894
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OFFSET
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1,1
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COMMENTS
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Are there infinitely many primitive doubly abundant numbers?
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LINKS
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EXAMPLE
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42 is a primitive doubly abundant number because it is abundant (s(42) = 54), the sum of its proper divisors is abundant (s(54) = 66) and no divisor of 42 is doubly abundant.
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MATHEMATICA
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s[n_] := DivisorSigma[1, n] - n; q[n_] := Module[{s1 = s[n]}, s1 > n && s[s1] > s1]; primQ[n_] := q[n] && !AnyTrue[Most[Divisors[n]], q]; Select[Range[900], primQ] (* Amiram Eldar, Mar 11 2024 *)
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PROG
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(Haskell)
import Data.List (intersect)
a125640 n = a125640_list !! (n-1)
a125640_list = f a125639_list [] where
f (x:xs) ys = if null (a027751_row' x `intersect` ys)
then x : f xs (x : ys) else f xs ys
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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Gabriel Cunningham (gabriel.cunningham(AT)gmail.com), Nov 28 2006
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EXTENSIONS
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STATUS
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approved
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