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%I #6 Aug 03 2014 20:34:14
%S 193,397,454,457,613,614,661,757,758,997,998,1093,1237,1238,1453,1478,
%T 1657,1681,1766,2137,2341,2413,2455,2593,2917,2918,2942,2966,3217,
%U 3334,3494,3589,4021,4177,4183,4406,4621,5143,5233,5965,6121,6133,6134,6193
%N Numbers n such that the numbers of divisors of n,n+1 and n+2 are k,2k,4k respectively for some k.
%H Harvey P. Dale, <a href="/A100363/b100363.txt">Table of n, a(n) for n = 1..1000</a>
%e n=193,195,195 have 2,4,8 divisors.
%t d0[x_] :=DivisorSigma[0, x];ta={{0}}; Do[g=n;s=d0[n];s1=d0[n+1];s2=d0[n+2]; If[Equal[s1, 2*s]&&Equal[s2, 4*s], ta=Append[ta, n]; Print[{n, s, s1, s2}]], {n, 1, 10000}];{ta=Delete[ta, 1], g}
%t Flatten[Position[Partition[DivisorSigma[0,Range[6200]],3,1],_?(Length[ Union[ #/{1,2,4}]] == 1&),{1},Heads->False]] (* _Harvey P. Dale_, Aug 03 2014 *)
%Y Cf. A000005, A063446.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 19 2004