A322254 Larger number of dihedral amicable pairs: numbers (m, n) such that t(m) = t(n) = m + n, where t(n) = sigma(n) + d(n).

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..32.

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.

Example

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.

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

Prog

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

Crossrefs

Cf. A007503, A083874, A320457.

Sequence in context: A031417 A361797 A260289 * A204278 A165677 A143076

Adjacent sequences: A322251 A322252 A322253 * A322255 A322256 A322257

Keyword

nonn

Author

Amiram Eldar, Dec 01 2018

Status

approved