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
Keywords
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.
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,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
Comments