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A322254 Greater members of dihedral amicable pairs: numbers (m, k) such that t(m) = t(k) = m + k, where t(k) = sigma(k) + d(k).

%I A322254 #17 Jul 03 2025 09:28:47
%S A322254 274,586,11470,18802,19270,22184,23288,39790,38744,65392,68476,163676,
%T A322254 198628,263890,463390,512116,596258,1070492,1100384,1342004,1590452,
%U A322254 2139722,2122946,2262628,2389562,2562844,2344436,2831470,2642656,2949628,3464008,5476346
%N A322254 Greater members of dihedral amicable pairs: numbers (m, k) such that t(m) = t(k) = m + k, where t(k) = sigma(k) + d(k).
%C A322254 Jensen and Bussian suggested the calculation of this sequence as a part of a student research project.
%C A322254 The terms are ordered according to their lesser counterparts (A320457). - _Amiram Eldar_, Jul 03 2025
%H A322254 Amiram Eldar, <a href="/A322254/b322254.txt">Table of n, a(n) for n = 1..420</a>
%H A322254 David W. Jensen and Michael K. Keane, <a href="https://apps.dtic.mil/sti/tr/pdf/ADA222857.pdf">A Number-Theoretic Approach to Subgroups of Dihedral Groups</a>, USAFA-TR-90-2, Air Force Academy Colorado Springs, Colorado, 1990.
%H A322254 David W. Jensen and Eric R. Bussian, <a href="http://www.jstor.org/stable/2686678">A Number-Theoretic Approach to Counting Subgroups of Dihedral Groups</a>, The College Mathematics Journal, Vol. 23, No. 2 (1992), pp. 150-152.
%e A322254 274 is in the sequence since (144, 274) is a pair of dihedral amicable numbers: sigma(144) + d(144) = 403 + 15 = 418, sigma(274) + d(274) = 414 + 4 = 418, and 144 + 274 = 418.
%t A322254 t[n_] := DivisorSigma[0,n] + DivisorSigma[1,n]-n; s={}; Do[n=t[m]; If[n>m && t[n]==m, AppendTo[s,n]], {m,1,100000}]; s
%o A322254 (PARI) f(n) = numdiv(n) + sigma(n) - n;
%o A322254 isok(n) = my(nn = f(n)); (nn < n) && (n == f(nn)); \\ _Michel Marcus_, Dec 04 2018
%Y A322254 Cf. A000005 (d), A000203 (sigma), A007503, A083874, A320457 (lesser members).
%K A322254 nonn
%O A322254 1,1
%A A322254 _Amiram Eldar_, Dec 01 2018