This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156942 #45 Jan 16 2025 03:06:07
%S A156942 11025,99225,245025,275625,342225,540225,893025,1334025,1863225,
%T A156942 2205225,2480625,3080025,3186225,3980025,4601025,4862025,5832225,
%U A156942 6125625,6890625,7868025,8037225,8555625,9272025,9828225,10595025,10989225
%N A156942 Odd abundant numbers whose abundance is odd.
%C A156942 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 A156942 Any term must be an odd square. Square roots are in A174830.
%C A156942 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
%C A156942 Question: Is this a subsequence of A379503? (Is A379504(a(n)) > 0 for all n? See A379951). The first 15000 terms are all included there. - _Amiram Eldar_ and _Antti Karttunen_, Jan 06 2025
%C A156942 Question 2: Is A379505(a(n)) > 1 for all n, especially if there are no quasiperfect numbers (numbers k such that sigma(k) = 2k+1)? - _Antti Karttunen_, Jan 06 2025
%C A156942 From _Amiram Eldar_, Jan 16 2025: (Start)
%C A156942 The least term that is not divisible by 5 is a(75) = 81162081.
%C A156942 The least term that is not divisible by 3 is a(296889) = 1382511906801025.
%C A156942 The least term that is coprime to 15 is 15285071557677427358507559514565648611799881. (End)
%H A156942 Amiram Eldar, <a href="/A156942/b156942.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert G. Wilson v)
%F A156942 a(n) = A174830(n)^2. - _M. F. Hasler_, Jan 26 2020
%t A156942 fQ[n_] := Block[{ds = DivisorSigma[1, n] - 2 n}, ds > 0 && OddQ@ ds]; Select[ Range[1, 12006223, 2], fQ @# &]
%o A156942 (PARI) is(n)=my(s=sigma(n)); n%2 && s>2*n && (s-2*n)%2 \\ _Charles R Greathouse IV_, Feb 21 2017
%Y A156942 Cf. A005101, A005231, A028982, A033880, A156903, A174830, A379503, A379504, A379505, A379951 [= A379504(a(n))].
%Y A156942 Subsequences: A156943, A325311 (thus also A379490), A347890, A379949 (terms that are primitive abundant).
%K A156942 nonn
%O A156942 1,1
%A A156942 _Robert G. Wilson v_, Feb 18 2009
%E A156942 Edited by _Robert G. Wilson v_ at the suggestion of _T. D. Noe_, Mar 30 2010