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

1,2

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A340017 A303606 A303661 * A030627 A177492 A077448

Adjacent sequences: A175388 A175389 A175390 * A175392 A175393 A175394

Keyword

nonn

Author

Leroy Quet, Apr 27 2010

Extensions

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

Status

approved