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A037020
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Numbers n such that sum of proper (or aliquot) divisors of n is a prime.
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12
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4, 8, 21, 27, 32, 35, 39, 50, 55, 57, 63, 65, 77, 85, 98, 111, 115, 125, 128, 129, 155, 161, 171, 175, 185, 187, 189, 201, 203, 205, 209, 221, 235, 237, 242, 245, 265, 275, 279, 291, 299, 305, 309, 319, 323, 324, 325, 327, 335, 338, 341, 365, 371, 377, 381
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Assuming the Goldbach conjecture, it is easy to show that all primes, except 2 and 5, are the sum of the proper divisors of some number. (T. D. Noe, Nov 29 2006).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| A001065(a(n)) is in A000040.
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EXAMPLE
| a(4)=27 because the aliquot divisors of 27 are 1 3 9, whose sum is 13, prime.
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MATHEMATICA
| Select[Range[400], PrimeQ[DivisorSigma[1, #]-#]&] (* From Harvey P. Dale, May 09 2011 *)
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PROG
| (Haskell)
import Data.List (elemIndices)
a037020 n = a037020_list !! (n-1)
a037020_list = map (+ 1) $ elemIndices 1 $ map (a010051 . a001065) [1..]
-- Reinhard Zumkeller, Sep 15 2011
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CROSSREFS
| Cf. A001065, A053868, A053869, A010051.
Sequence in context: A168451 A000585 A102559 * A094878 A079860 A006908
Adjacent sequences: A037017 A037018 A037019 * A037021 A037022 A037023
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Felice Russo (frusso(AT)micron.com)
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