A228009 The number of n-digit numbers whose first k digits are divisible by k^2 for k = 1..n.

9, 22, 24, 16, 7, 7, 1

Offset

1,1

Comments

There are total 86 numbers and 6480005 is the only 7-digit number to satisfy the requirement.

Links

Table of n, a(n) for n=1..7.

Example

There are nine one-digit numbers divisible by 1 so a(1)=9.
For two-digit numbers, the second digit must make it divisible by 2^2, which gives 22 numbers: 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 to satisfy the requirement. So a(2)=22.

Mathematica

a = Table[j, {j, 9}]; r = 2; t = {}; While[! a == {}, n = Length[a]; k = 1; b = {}; While[! k > n, z0 = a[[k]]; Do[z = 10*z0 + j; If[Mod[z, r*r] == 0, b = Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, n]; a = b; r++]; t

Crossrefs

Cf. A079042.

Sequence in context: A250729 A251292 A177458 * A330477 A295008 A154528

Adjacent sequences: A228006 A228007 A228008 * A228010 A228011 A228012

Keyword

nonn,base,fini,full

Author

Shyam Sunder Gupta, Aug 08 2013

Status

approved