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).

274, 586, 11470, 18802, 19270, 22184, 23288, 39790, 38744, 65392, 68476, 163676, 198628, 263890, 463390, 512116, 596258, 1070492, 1100384, 1342004, 1590452, 2139722, 2122946, 2262628, 2389562, 2562844, 2344436, 2831470, 2642656, 2949628, 3464008, 5476346

Offset: 1

Author

Amiram Eldar, Dec 01 2018

Keywords

• nonn

Comments

Jensen and Bussian suggested the calculation of this sequence as a part of a student research project.

The terms are ordered according to their lesser counterparts (A320457). - Amiram Eldar, Jul 03 2025

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..420
• David W. Jensen and Michael K. Keane, A Number-Theoretic Approach to Subgroups of Dihedral Groups, USAFA-TR-90-2, Air Force Academy Colorado Springs, Colorado, 1990.
• David W. Jensen and Eric R. Bussian, A Number-Theoretic Approach to Counting Subgroups of Dihedral Groups, The College Mathematics Journal, Vol. 23, No. 2 (1992), pp. 150-152.

Crossrefs

Cf. A000005 (d), A000203 (sigma), A007503, A083874, A320457 (lesser members).

Programs

Mathematica

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

PARI

f(n) = numdiv(n) + sigma(n) - n;
isok(n) = my(nn = f(n)); (nn < n) && (n == f(nn)); \\ Michel Marcus, Dec 04 2018