A115557 Squares in A076361.

1, 49, 121, 169, 361, 529, 841, 961, 1849, 2209, 2809, 5329, 6889, 9409, 10609, 12769, 16129, 24649, 32041, 38809, 39601, 49729, 51529, 54289, 57121, 58081, 63001, 66049, 73441, 78961, 96721, 99856, 100489, 110889, 124609, 151321, 160801

Offset: 1

Author

Labos Elemer, Jan 25 2006

Keywords

• nonn

Comments

The commutator [sigma, tau] is zero, that is, A076360(x) = 0 and x is a square.

Examples

			The special squared prime 121 is a term because it is a square and sigma(tau(121)) = sigma(3) = 4 = tau(sigma(121)) = tau(1 + 11 + 121) = tau(133) = 4.
The least solution with composite square root is 316^2 = 99856: tau(99856) = 15, sigma(15) = 24 or sigma(99856) = 195951 = 3*7*7*31*43, tau(195951) = 24.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A062068, A062069, A076360, A076361, A115558.

Programs

Mathematica

ds = DivisorSigma; Select[Range[1000]^2, ds[0, ds[1, #]] == ds[1, ds[0, #]] &] (* Giovanni Resta, Apr 29 2017 *)

PARI

isok(n) = issquare(n) && (sigma(numdiv(n)) == numdiv(sigma(n))); \\ Michel Marcus, Dec 20 2013

Formula

a(n) = A115558(n)^2. - Amiram Eldar, Jan 31 2025