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%I #23 Dec 08 2020 02:34:15
%S 3,8,22,24,66,70,76,94,115,119,170,210,214,217,228,252,265,282,310,
%T 316,322,345,357,382,385,490,497,510,517,522,527,580,612,642,651,679,
%U 710,716,742,745,782,795,801,833,862,889,920,930,935,948,952,966,970
%N Sum of unitary divisors of n is a square > 1.
%C A unitary divisor of n is a divisor d of n such that gcd(d, n/d) = 1.
%H Amiram Eldar, <a href="/A063937/b063937.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F a(n) > 1 and A010052(A034448(a(n))) = 1. - _Reinhard Zumkeller_, Aug 15 2012
%e The unitary divisors of 3 are 1,3 and then 3 + 1 = 4 is a square.
%t udQ[n_]:=Module[{totdivs=Total[Sort[Flatten[Outer[Times,Sequence@@({1,#}&/@Power@@@FactorInteger[n])]]]]},totdivs>1&&IntegerQ[Sqrt[totdivs]]]; Select[Range[1000],udQ] (* _Harvey P. Dale_, Apr 22 2012, using program from Eric Weisstein at http://mathworld.wolfram.com/UnitaryDivisor.html *)
%o (PARI) us(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
%o { n=0; for (m=1, 10^9, u=us(m); if (issquare(u) && u > 1, write("b063937.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 03 2009
%o (Haskell)
%o import Data.List (findIndices)
%o a063937 n = a063937_list !! (n-1)
%o a063937_list = map (+ 2) $
%o findIndices ((== 1) . a010052) $ tail a034448_list
%o -- _Reinhard Zumkeller_, Aug 15 2012
%Y Cf. A034448, A063936.
%K easy,nice,nonn
%O 1,1
%A _Felice Russo_, Aug 31 2001
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