A105351 - OEIS

%I #31 Apr 26 2023 18:23:34

%S 1,2,8,4,4,16,4,32,20,2,16,12,12,4,24,2,32,64,128,16,96,32,16,64,32,4,

%T 32,32,16,96,32,8,256,2,16,60,8,32,12,64,48,480,32,128,512,16,128,192,

%U 2,128,96,32,64,160,64,16,6,64,64

%N Number of divisors of 135...(2n-1), the concatenation of the first n odd numbers.

%H Sean A. Irvine, <a href="/A105351/b105351.txt">Table of n, a(n) for n = 1..84</a>

%e The number of divisors of 13 is 2, hence a(2) = 2.

%e The number of divisors of 135 is 8, hence a(3) = 8.

%e The number of divisors of 1357 is 4, hence a(4) = 4.

%p R:= 1: x:= 1:

%p for n from 2 to 49 do

%p   x:= x*10^(1+ilog10(2*n-1)) + 2*n - 1;

%p R:= R, numtheory:-tau(x);

%p od:

%p R; # _Robert Israel_, Mar 02 2023

%t ParallelTable[Divisors[FromDigits[Join@@IntegerDigits/@Table[1+2*k,{k,0,n}]]]//Length,{n,0,48}] (* _J.W.L. (Jan) Eerland_, Mar 02 2023 *)

%K base,nonn,more

%O 1,2

%A _Parthasarathy Nambi_, Apr 30 2005, Jul 01 2005

%E Edited by _N. J. A. Sloane_, Aug 23 2008 at the suggestion of _R. J. Mathar_

%E a(18)-a(50) from _J.W.L. (Jan) Eerland_, Mar 02 2023

%E a(51)-a(58) from _Jon E. Schoenfield_, Mar 03 2023

%E Offset corrected by _Sean A. Irvine_, Mar 24 2023