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A115557 Squares in A076361. 4
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 (list; graph; refs; listen; history; text; internal format)
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 prime square 121 is here 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: A163245 A084733 A227863 * A167718 A080665 A130007

Adjacent sequences:  A115554 A115555 A115556 * A115558 A115559 A115560

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 25 2006

STATUS

approved

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Last modified July 28 12:48 EDT 2017. Contains 289889 sequences.