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%I #20 Jan 14 2022 06:34:26
%S 11025,99225,245025,275625,342225,540225,893025,1334025,1863225,
%T 2205225,2480625,3080025,3186225,3980025,4601025,4862025,5832225,
%U 6125625,6890625,7868025,8037225,8555625,9272025,9828225,10595025,10989225
%N Odd abundant numbers whose abundance is odd.
%C Number of terms <10^n: 0, 0, 0, 0, 2, 7, 24, 83, 250, 792, 2484, 7988, 25383, 80082, ..., . Not all are a multiple of 25, i.e.; 81162081 = 9009^2 = (9*7*11*13)^2. See A156943.
%C Any term must be an odd square. Square roots are in A174830.
%C Indeed, the sum of divisors of any number isn't odd unless it's a square or twice a square (A028982), and to get the abundance, twice the number is subtracted, so the parity remains the same. - _M. F. Hasler_, Jan 26 2020
%H Amiram Eldar, <a href="/A156942/b156942.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from R. G. Wilson v)
%F a(n) = A174830(n)^2. - _M. F. Hasler_, Jan 26 2020
%t fQ[n_] := Block[{ds = DivisorSigma[1, n] - 2 n}, ds > 0 && OddQ@ ds]; Select[ Range[1, 12006223, 2], fQ @# &]
%o (PARI) is(n)=my(s=sigma(n)); n%2 && s>2*n && (s-2*n)%2 \\ _Charles R Greathouse IV_, Feb 21 2017
%Y Cf. A028982, A033880, A156903, A156943, A174830.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Feb 18 2009
%E Edited by _Robert G. Wilson v_ at the suggestion of _T. D. Noe_, Mar 30 2010
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