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Numbers n (other than powers of 2) such that the absolute value of abundance(n) is a square.
1

%I #15 Feb 16 2025 08:33:13

%S 5,6,12,14,17,28,37,38,44,70,88,92,98,101,108,110,134,152,168,170,172,

%T 197,206,220,248,257,284,348,374,398,401,410,428,434,496,550,577,580,

%U 590,604,632,638,677,726,748,752,798,884,910,918,952,974,988,1032

%N Numbers n (other than powers of 2) such that the absolute value of abundance(n) is a square.

%H Arkadiusz Wesolowski, <a href="/A185031/b185031.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Abundance.html">Abundance</a>

%t lst = {}; e = 10; Do[If[IntegerQ[Abs[DivisorSigma[1, n] - 2*n]^(1/2)], AppendTo[lst, n]], {n, 2^e + e}]; Complement[lst, Table[Power[2, m], {m, 0, e}]]

%Y Supersequence of A188484.

%K nonn,changed

%O 1,1

%A _Arkadiusz Wesolowski_, Jan 23 2012