A100363 Numbers n such that the numbers of divisors of n,n+1 and n+2 are k,2k,4k respectively for some k.

193, 397, 454, 457, 613, 614, 661, 757, 758, 997, 998, 1093, 1237, 1238, 1453, 1478, 1657, 1681, 1766, 2137, 2341, 2413, 2455, 2593, 2917, 2918, 2942, 2966, 3217, 3334, 3494, 3589, 4021, 4177, 4183, 4406, 4621, 5143, 5233, 5965, 6121, 6133, 6134, 6193

Offset: 1

Author

Labos Elemer, Nov 19 2004

Keywords

• nonn

Examples

			n=193,195,195 have 2,4,8 divisors.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A063446.

Programs

Mathematica

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}
Flatten[Position[Partition[DivisorSigma[0,Range[6200]],3,1],?(Length[ Union[ #/{1,2,4}]] == 1&),{1},Heads->False]] (* _Harvey P. Dale, Aug 03 2014 *)