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Numbers n such that sigma(n) and sigma(sigma(n)) are both perfect squares.
1

%I #13 Aug 15 2019 12:25:16

%S 1,343,10680,11448,11832,12760,12920,13470,14360,14526,15064,15198,

%T 15486,15752,16194,16264,16376,16390,16472,16910,17110,18734,20366,

%U 20654,20822,21094,21122,21158,21598,21843,22899,23403,23691,24695

%N Numbers n such that sigma(n) and sigma(sigma(n)) are both perfect squares.

%H Giovanni Resta, <a href="/A134263/b134263.txt">Table of n, a(n) for n = 1..2000</a> (first 77 terms from Amiram Eldar)

%e sigma(343) = 400 = 20^2 and sigma(400) = 961 = 31^2, so 343 belongs to the sequence.

%t l = {}; For[i = 1, i <= 10^6, i++, a = DivisorSigma[1, i]; b = DivisorSigma[1, a]; If[IntegerQ[a^(1/2)] && IntegerQ[b^(1/2)], l = Append[l, i]]]; l

%o (PARI) isok(n) = issquare(sigma(n)) && issquare(sigma(sigma(n))); \\ _Michel Marcus_, Aug 15 2019

%Y Subsequence of A006532.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Jan 14 2008