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Numbers k such that the deficiency of k^2 is itself a square.
4

%I #17 Jul 27 2017 02:39:25

%S 1,2,4,8,16,32,46,64,128,256,284,512,1024,1633,2048,4096,8192,16384,

%T 32768,65536,131072,149728,242656,260495,262144,298057,524288,1048576,

%U 1056752,2097152,4194304,8388608,9587584,16777216,17706256,33554432,67108864,134217728

%N Numbers k such that the deficiency of k^2 is itself a square.

%C The sequence of square roots of the deficiencies of this sequence is A288145.

%C The current sequence is the disjoint union of the powers of 2 (A000079) and the sequence A289274.

%H Giovanni Resta, <a href="/A289275/b289275.txt">Table of n, a(n) for n = 1..58</a>

%t Select[Range[10^5], IntegerQ@ Sqrt[2 #^2 - DivisorSigma[1, #^2]] &] (* _Michael De Vlieger_, Jul 04 2017 *)

%o (PARI) isok(n) = issquare(2*n^2 - sigma(n^2)); \\ _Michel Marcus_, Jul 01 2017

%Y Disjoint union of the sequences A000079 and A289274.

%Y Square roots of deficiencies of squares is A288145.

%K nonn

%O 1,2

%A _Jens Voß_, Jun 30 2017

%E a(35)-a(38) from _Giovanni Resta_, Jul 27 2017