A100364 Numbers n such that the numbers of divisors of n,n+1,n+2 and n+3 are k,2k,4k,8k respectively for some k.

613, 757, 997, 1237, 2917, 6133, 9853, 15733, 19477, 22501, 24421, 25237, 26293, 26437, 28117, 31477, 33301, 35317, 44101, 45061, 46357, 51637, 53077, 56701, 59221, 61653, 61717, 64381, 65917, 66853, 68583, 70501, 70887, 72901, 75133

Offset: 1

Author

Labos Elemer, Nov 19 2004

Keywords

• nonn

Examples

			n=613,614,615,616 have 2,4,8,16 divisors respectively.
		

Links

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

Crossrefs

Cf. A000005, A063446, A100363.

Programs

Mathematica

d0[x_] :=DivisorSigma[0, x];ta={{0}}; Do[g=n;s=d0[n];s1=d0[n+1];s2=d0[n+2];s3=d0[n+3] If[Equal[s1, 2*s]&&Equal[s2, 4*s]&&Equal[s3, 8*s], ta=Append[ta, n]; Print[{n, s, s1, s2, s3}]], {n, 1, 1000000}];{ta=Delete[ta, 1], g}
nd2Q[{a_,b_,c_,d_}]:={b,c,d}/a=={2,4,8}; Position[Partition[ DivisorSigma[ 0,Range[80000]],4,1],?(nd2Q[#]&)]//Flatten (* _Harvey P. Dale, Feb 25 2020 *)