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 A322256 Number such that t(n) = t(n+1) where t(n) = tau(n) + sigma(n) = A007503(n) is the number of subgroups of the dihedral group of order 2n. 0
 14, 1334, 1634, 2685, 33998, 42818, 64665, 84134, 109214, 122073, 166934, 289454, 383594, 440013, 544334, 605985, 649154, 655005, 792855, 845126, 1642154, 2284814, 2305557, 2913105, 3571905, 3682622, 4701537, 5181045, 6431732, 6444873, 6771405, 10074477 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Jensen and Keane asked if this sequence is infinite. Jensen and Bussian suggested the calculation of this sequence as a part of a student research project. Supersequence of A054004. Terms that are not in it are 845126, 14392646, 10461888478, ... LINKS 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. MATHEMATICA t[n_] := DivisorSigma[0, n] + DivisorSigma[1, n]; tQ[n_] := t[n] == t[n + 1]; Select[Range, tQ] PROG (PARI) isok(n) = (numdiv(n)+sigma(n)) == (numdiv(n+1)+sigma(n+1)); \\ Michel Marcus, Dec 04 2018 (MAGMA) [n: n in [1..2*10^6] | (NumberOfDivisors(n) + SumOfDivisors(n)) eq (NumberOfDivisors(n+1) + SumOfDivisors(n+1))]; // Vincenzo Librandi, Dec 08 2018 CROSSREFS Cf. A007503, A054004, A083874. Sequence in context: A209677 A137603 A160107 * A054004 A280087 A240703 Adjacent sequences:  A322253 A322254 A322255 * A322257 A322258 A322259 KEYWORD nonn AUTHOR Amiram Eldar, Dec 01 2018 STATUS approved

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Last modified October 21 17:02 EDT 2021. Contains 348155 sequences. (Running on oeis4.)