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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A000005, A063446, A100363.

Sequence in context: A253441 A253158 A159641 * A142435 A090869 A020372

Adjacent sequences: A100361 A100362 A100363 * A100365 A100366 A100367

Keyword

nonn

Author

Labos Elemer, Nov 19 2004

Status

approved