A222812 Number of n-digit numbers N such that the number formed by some nontrivial permutation of the digits of N divides N.

0, 18, 329, 5000, 65931, 779504, 8517616, 88555255, 897147508, 8997325290, 90000000000, 900000000000, 9000000000000, 90000000000000, 900000000000000, 9000000000000000, 90000000000000000, 900000000000000000, 9000000000000000000, 90000000000000000000

Offset

1,2

Comments

Suggested by A214927.

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (10).

Formula

a(n) = 9 * 10^(n-1) for n >= 11. - Hiroaki Yamanouchi, Sep 03 2014.

G.f.: x^2*(26747100*x^9 +25850210*x^8 +11594958*x^7 +3379095*x^6 +722576*x^5 +120194*x^4 +15931*x^3 +1710*x^2 +149*x +18)/(1-10*x). - Robert Israel, Sep 03 2014

Example

Some of the smallest solutions are:
[10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99] (so a(2) = 18),
[100, 101, 105, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 130, 131, 133, 140, 141, 144, 150, 151, 155, 160, 161, 166, 170, 171, 177, 180, 181, 188, 190, 191, 199, 200, 202, 210, 211, 212, 220, 221, 222, 223, 224, ...]
Note that 11 is in the sequence because permuting the two digits gives 11, and 11 divides 11.

Crossrefs

Cf. A214927, A222809, A222810, A222811.

Sequence in context: A223311 A041145 A041614 * A166787 A280806 A068771

Adjacent sequences: A222809 A222810 A222811 * A222813 A222814 A222815

Keyword

nonn,base

Author

N. J. A. Sloane, Mar 10 2013

Extensions

a(7)-a(20) from Hiroaki Yamanouchi, Sep 03 2014

Status

approved