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

1,2

Links

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

Formula

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

Example

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 first 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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A338499 A227863 A339131 * A167718 A080665 A130007

Adjacent sequences: A115554 A115555 A115556 * A115558 A115559 A115560

Keyword

nonn

Author

Labos Elemer, Jan 25 2006

Status

approved