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sigma(n) + n is a square.
2

%I #12 Aug 13 2019 11:22:32

%S 33,90,385,420,649,900,1441,1464,1480,1729,2025,2616,3168,3588,3984,

%T 4005,4873,5049,5185,6225,7153,7585,8740,9060,10285,11080,12280,12609,

%U 13914,14809,15136,16065,16345,17017,17353,17809,18073,18625,19098

%N sigma(n) + n is a square.

%H Amiram Eldar, <a href="/A114069/b114069.txt">Table of n, a(n) for n = 1..10000</a>

%e sigma(33) + 33 = 81 = 9^2.

%t Select[Range[20000],IntegerQ[Sqrt[DivisorSigma[1,#]+#]]&] (* _Harvey P. Dale_, May 09 2011 *)

%o (PARI) isok(n) = issquare (n+sigma(n)); \\ _Michel Marcus_, Aug 13 2019

%Y Cf. A000203, A155085.

%K nonn

%O 1,1

%A _Giovanni Resta_, Feb 13 2006