cp's OEIS Frontend

A320457 Lesser members of dihedral amicable pairs: numbers (m, k) such that t(m) = t(k) = m + k, where t(k) = sigma(k) + d(k).

%I A320457 #37 Jul 03 2025 09:28:41
%S A320457 144,300,10434,15774,17034,21032,22088,35394,36872,65324,67628,153868,
%T A320457 188468,254526,379026,483812,492414,905212,1090528,1198180,1514212,
%U A320457 1634262,1886046,1898420,2013414,2184860,2191588,2316546,2596448,2816156,3340024,3854886
%N A320457 Lesser members of dihedral amicable pairs: numbers (m, k) such that t(m) = t(k) = m + k, where t(k) = sigma(k) + d(k).
%C A320457 Jensen and Bussian suggested the calculation of this sequence as a part of a student research project.
%H A320457 Amiram Eldar, <a href="/A320457/b320457.txt">Table of n, a(n) for n = 1..420</a>
%H A320457 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 A320457 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 A320457 144 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 A320457 t[n_] := DivisorSigma[0,n] + DivisorSigma[1,n] - n; s={}; Do[n = t[m]; If[n>m && t[n]==m, AppendTo[s,m]], {m, 1, 100000}];s
%o A320457 (PARI) f(n) = numdiv(n) + sigma(n) - n;
%o A320457 isok(n) = my(nn = f(n)); (nn > n) && (n == f(nn)); \\ _Michel Marcus_, Dec 04 2018
%Y A320457 Cf. A000005 (d), A000203 (sigma), A007503, A083874, A322254 (greater members).
%K A320457 nonn
%O A320457 1,1
%A A320457 _Amiram Eldar_, Dec 01 2018