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
Keywords
Examples
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.
Crossrefs
Cf. A000005.
Programs
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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 *)
Extensions
Some terms corrected by Giovanni Resta, Apr 28 2013
Comments