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A063936
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Numbers k such that the sum of unitary proper divisors of k is a square > 1.
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4
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15, 26, 44, 56, 95, 96, 119, 122, 124, 140, 143, 194, 215, 216, 236, 287, 304, 364, 386, 407, 495, 511, 527, 551, 556, 560, 575, 639, 740, 752, 764, 780, 791, 794, 815, 871, 900, 935, 936, 992, 1004, 1036, 1116, 1159, 1196, 1199, 1232, 1295, 1328, 1346
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OFFSET
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1,1
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COMMENTS
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A unitary divisor of n is a divisor d of n such that gcd(d, n/d) = 1.
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LINKS
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FORMULA
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EXAMPLE
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The unitary divisors of 15 are 1,3,5,15 and then the unitary aliquot part is 9 which is a square.
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MATHEMATICA
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us[1] = 0; us[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n; Select[Range[1500], (s = us[#]) > 1 && IntegerQ@Sqrt[s] &] (* Amiram Eldar, Mar 14 2020 *)
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PROG
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(PARI) us(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
j=[]; for(n=1, 3000, if(us(n)-n > 1 && issquare(us(n)-n), j=concat(j, n))); j
(PARI) us(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
{ n=0; for (m=1, 10^9, u=us(m) - m; if (issquare(u) && u > 1, write("b063936.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 03 2009
(Haskell)
import Data.List (findIndices)
a063936 n = a063936_list !! (n-1)
a063936_list = map (+ 1) $
findIndices (\x -> x > 1 && a010052 x == 1) a034460_list
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CROSSREFS
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KEYWORD
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easy,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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