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A094342 Successive record-setters for tau(n+1)*tau(n-1)/tau(n)^2, where tau(n) is the number of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified May 23 14:23 EDT 2024. Contains 372763 sequences. (Running on oeis4.)