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%I #24 Nov 28 2023 10:49:22
%S 1,6,10,14,15,16,21,22,26,33,34,35,36,38,39,46,51,55,57,58,62,65,69,
%T 74,77,81,82,85,86,87,91,93,94,95,100,106,111,115,118,119,122,123,129,
%U 133,134,141,142,143,145,146,155,158,159,161,166,177,178,183,185,187,194
%N Numbers k such that the number of divisors of k^2 is a square.
%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 3, 35, 326, 3275, 33090, 332435, 3327555, 33283964, 332868092, 3328794682, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3328... . - _Amiram Eldar_, Nov 28 2023
%H Amiram Eldar, <a href="/A063774/b063774.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F {n: A048691(n) in A000290}. - _R. J. Mathar_, Aug 09 2012
%e n=2: a(2) = 6 because the number of divisors of 6^2 is 9, a square.
%t Select[Range[200],IntegerQ[Sqrt[DivisorSigma[0,#^2]]]&] (* _Harvey P. Dale_, Jun 06 2012 *)
%o (PARI) j=[]; for(n=1,500,a=numdiv(n^2); if(issquare(a),j=concat(j,n))); j
%o (PARI) n=0; for (m=1, 10^9, if(issquare(numdiv(m^2)), write("b063774.txt", n++, " ", m); if (n==1000, break))) \\ _Harry J. Smith_, Aug 30 2009
%o (PARI) is(n)=my(f=factor(n)[,2]); issquare(prod(i=1,#f,2*f[i]+1)) \\ _Charles R Greathouse IV_, Sep 18 2015
%Y Cf. A000290, A048691.
%Y Subsequences: A030229, A238748.
%K easy,nonn
%O 1,2
%A _Jason Earls_, Aug 15 2001
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