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A222812
Number of n-digit numbers N such that the number formed by some nontrivial permutation of the digits of N divides N.
4
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.
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
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Mar 10 2013
EXTENSIONS
a(7)-a(20) from Hiroaki Yamanouchi, Sep 03 2014
STATUS
approved