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
Keywords
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.
Programs
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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
Comments