A054004 Numbers k such that k and k+1 have the same number and sum of divisors.

14, 1334, 1634, 2685, 33998, 42818, 64665, 84134, 109214, 122073, 166934, 289454, 383594, 440013, 544334, 605985, 649154, 655005, 792855, 1642154, 2284814, 2305557, 2913105, 3571905, 3682622, 4701537, 5181045, 6431732, 6444873, 6771405, 10074477, 10118654, 10195305, 12825266, 15751533

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1831 (calculated using the b-file at A002961; terms 1..967 from T. D. Noe)

Example

Divisors of 14 = {1, 2, 7, 14}, divisors of 15 = {1, 3, 5, 15}, both have four divisors and sum = 24.

Mathematica

Select[Range[100000], DivisorSigma[0, #] == DivisorSigma[0, # + 1] && DivisorSigma[1, #] == DivisorSigma[1, # + 1] &] (* Jayanta Basu, Mar 20 2013 *)

Prog

(PARI) isok(k) = (sigma(k) == sigma(k+1)) && (numdiv(k) == numdiv(k+1)); \\ Michel Marcus, Mar 04 2026

Crossrefs

Cf. A000005, A000203, A002961, A005237, A053249, A054005, A054006, A054007.

Sequence in context: A137603 A160107 A322256 * A280087 A240703 A240640

Adjacent sequences: A054001 A054002 A054003 * A054005 A054006 A054007

Keyword

nonn

Author

Asher Auel, Jan 12 2000

Extensions

More terms from Jud McCranie, Jun 02 2000

More terms from Amiram Eldar, Jul 17 2022

Status

approved