A225004 a(n) is the largest multiple of n with fewer than twice as many divisors as n.

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

Offset

1,2

Comments

Conjecture: a(n) is 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, i-1]; v[[i]]++]]]; r[e, Length@e]; mu]]; Array[a, 46] (* Giovanni Resta, Apr 28 2013 *)

Crossrefs

Cf. A000005.

Sequence in context: A081403 A259602 A017668 * A339857 A074373 A067115

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