A175391 Perfect squares having a square number of divisors.

1, 36, 100, 196, 225, 256, 441, 484, 676, 1089, 1156, 1225, 1296, 1444, 1521, 2116, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929, 6561, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 10000, 11236, 12321, 13225, 13924, 14161, 14884, 15129

Offset: 1

Author

Leroy Quet, Apr 27 2010

Keywords

• nonn

Comments

From Robert Israel, Mar 20 2018: (Start)

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

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)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A063774, A175050. - Leroy Quet, May 16 2010

Programs

Maple

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

Mathematica

Select[Range[150], IntegerQ[Sqrt[DivisorSigma[0, #^2]]]&]^2 (* Vincenzo Librandi, Mar 21 2018 *)
Select[Range[150]^2,IntegerQ[Sqrt[DivisorSigma[0,#]]]&] (* Harvey P. Dale, Aug 16 2025 *)

PARI

isok(n) = issquare(n) && issquare(numdiv(n)); \\ Michel Marcus, Mar 21 2018

Formula

a(n) = A063774(n)^2. - Leroy Quet, May 16 2010

Extensions

Extended by Emeric Deutsch and Jon E. Schoenfield, May 11 2010