A094342 Successive record-setters for tau(n+1)*tau(n-1)/tau(n)^2, where tau(n) is the number of divisors of n.

2, 3, 5, 7, 11, 17, 19, 29, 41, 71, 181, 239, 379, 449, 701, 881, 1429, 1871, 2729, 3079, 4159, 10529, 11969, 23561, 40699, 51679, 90271, 104651, 146719, 226799, 244529, 252449, 388961, 403649, 825551, 906751, 1276001, 2408561, 2648449, 3807649, 4058209, 4406401

Offset

1,1

Comments

Most terms are primes. These are numbers with few factors which are sandwiched between numbers with many factors. Terms <379 are same as those of A090481.

Links

Amiram Eldar, Table of n, a(n) for n = 1..61

Example

tau(16)*tau(18)/tau(17)^2 = 5*6/2^2 = 15/2 and this is larger than for any n < 17, so 17 is in the sequence.

Maple

f := x -> tau(x-1)*tau(x+1)/tau(x)^2:?print m := 1: A := []: for k from 2 to 10^6 do if f(k) > m then m := f(k): A := [op(A), [k, f(k)]]: fi; od;

Mathematica

s = {}; d1 = 1; d2 = 2; rm = 0; Do[d3 = DivisorSigma[0, n]; r = d1*d3/d2^2; If[r > rm, rm = r; AppendTo[s, n - 1]]; d1 = d2; d2 = d3, {n, 3, 10000}]; s (* Amiram Eldar, Aug 28 2019 *)

Crossrefs

Cf. A090481.

Sequence in context: A335325 A189828 A090481 * A164641 A058982 A040069

Adjacent sequences: A094339 A094340 A094341 * A094343 A094344 A094345

Keyword

easy,nonn

Author

Isabel C. Lugo (isabel(AT)mit.edu), Jun 04 2004

Extensions

a(1) = 2 and more terms added by Amiram Eldar, Aug 28 2019

Status

approved