

A094342


Successive recordsetters for tau(n+1)*tau(n1)/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
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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(x1)*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



KEYWORD

easy,nonn


AUTHOR

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


EXTENSIONS



STATUS

approved



