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).

144, 300, 10434, 15774, 17034, 21032, 22088, 35394, 36872, 65324, 67628, 153868, 188468, 254526, 379026, 483812, 492414, 905212, 1090528, 1198180, 1514212, 1634262, 1886046, 1898420, 2013414, 2184860, 2191588, 2316546, 2596448, 2816156, 3340024, 3854886

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.

Examples

			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.
		

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, A322254 (greater 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,m]], {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