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.

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

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

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.

Mathematica

t[n_] := DivisorSigma[0, n] + DivisorSigma[1, n]; tQ[n_] := t[n] == t[n + 1]; Select[Range[1000000], 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