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

Author

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

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A090481.

Programs

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 *)

Extensions

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