A076289 - OEIS

%I #14 May 20 2024 02:34:09

%S 1,11,101,111,1001,1111,10001,10101,11111,100001,111111,1000001,

%T 1001001,1010101,1111111,10000001,11111111,100000001,100010001,

%U 101010101,111111111,1000000001,1001001001,1111111111,10000000001,10000100001,10101010101,11111111111

%N Numbers of the form (10^(m*r)-1)/(10^r-1) for positive integers m, r.

%H Robert Israel, <a href="/A076289/b076289.txt">Table of n, a(n) for n = 1..7046</a>

%H T. Chinburg and M. Henriksen, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa29/aa2932.pdf">Sums of k-th powers in the ring of polynomials with integer coefficients</a>, Acta Arithmetica, 29 (1976), 227-250.

%p N::= 20: # for terms <= 10^N

%p R:= {1}:

%p for n from 1 to 2*N do

%p   R:= R union select(`<=`, {seq((10^n-1)/(10^d-1), d = numtheory:-divisors(n))},10^N);

%p od:

%p sort(convert(R,list)); # _Robert Israel_, May 19 2024

%Y Cf. A064896 (k=2), A076270 (k=3), A076275 (k=4), A076284 (k=5), A076285 (k=6), A076286 (k=7), A076287 (k=8), A076288 (k=9), A076289 (k=10).

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 06 2002