

A225004


Largest multiple of n with less than twice as many divisors as n.


0



1, 4, 9, 16, 25, 18, 49, 64, 81, 50, 121, 48, 169, 98, 75, 256, 289, 162, 361, 100, 147, 242, 529, 192, 625, 338, 729, 196, 841, 150, 961, 1024, 363, 578, 245, 324, 1369, 722, 507, 400, 1681, 294, 1849, 484, 405, 1058, 2209, 768, 2401, 1250, 867, 676, 2809
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Conjecture: always a divisor of n^2.


LINKS

Table of n, a(n) for n=1..53.


EXAMPLE

a(6) = 18 because 6 has 4 divisors and term must have fewer than 8 divisors. Only 6, 12, and 18 are multiples of 6 with fewer than 8 divisors.


MATHEMATICA

a[n_] := If[n == 1, 1, Block[{nd, p, e, r, mu=0}, {p, e} = Transpose@ FactorInteger@ n; nd = 2*Times @@ (1+e); r[w_, i_] := Block[{v = w}, If[i < 1, mu = Max[mu, Times @@ (p^w)], While[Times @@ (1 + v) < nd, r[v, i1]; v[[i]]++]]]; r[e, Length@e]; mu]]; Array[a, 46] (* Giovanni Resta, Apr 28 2013 *)


CROSSREFS

Sequence in context: A081403 A259602 A017668 * A074373 A067115 A061077
Adjacent sequences: A225001 A225002 A225003 * A225005 A225006 A225007


KEYWORD

nonn


AUTHOR

J. Lowell, Apr 23 2013


EXTENSIONS

Some terms corrected by Giovanni Resta, Apr 28 2013


STATUS

approved



