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Perfect squares having a square number of divisors.
2

%I #24 Mar 21 2018 04:34:46

%S 1,36,100,196,225,256,441,484,676,1089,1156,1225,1296,1444,1521,2116,

%T 2601,3025,3249,3364,3844,4225,4761,5476,5929,6561,6724,7225,7396,

%U 7569,8281,8649,8836,9025,10000,11236,12321,13225,13924,14161,14884,15129

%N Perfect squares having a square number of divisors.

%C From _Robert Israel_, Mar 20 2018: (Start)

%C If m and n are coprime members of the sequence, then m*n is in the sequence.

%C Includes all numbers of the forms p^(4*i*(i+1)) and p^(2*i)*q^(2*i) where p, q are distinct primes and i is a positive integer. (End)

%H Robert Israel, <a href="/A175391/b175391.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A063774(n)^2. - _Leroy Quet_, May 16 2010

%p with(numtheory): a := proc (n) if type(sqrt(tau(n^2)), integer) = true then n^2 else end if end proc: seq(a(n), n = 1 .. 130); # _Emeric Deutsch_, May 11 2010

%t Select[Range[150], IntegerQ[Sqrt[DivisorSigma[0, #^2]]]&]^2 (* _Vincenzo Librandi_, Mar 21 2018 *)

%o (PARI) isok(n) = issquare(n) && issquare(numdiv(n)); \\ _Michel Marcus_, Mar 21 2018

%Y Cf. A063774, A175050. - _Leroy Quet_, May 16 2010

%K nonn

%O 1,2

%A _Leroy Quet_, Apr 27 2010

%E Extended by _Emeric Deutsch_ and _Jon E. Schoenfield_, May 11 2010