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%I #24 Mar 17 2022 07:07:04
%S 1,4,9,16,25,18,49,64,81,50,121,48,169,98,75,256,289,162,361,100,147,
%T 242,529,192,625,338,729,196,841,150,961,1024,363,578,245,324,1369,
%U 722,507,400,1681,294,1849,484,405,1058,2209,768,2401,1250,867,676,2809
%N a(n) is the largest multiple of n with fewer than twice as many divisors as n.
%C Conjecture: a(n) is always a divisor of n^2.
%e 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.
%t 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 *)
%Y Cf. A000005.
%K nonn
%O 1,2
%A _J. Lowell_, Apr 23 2013
%E Some terms corrected by _Giovanni Resta_, Apr 28 2013
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