A113999 - OEIS

%I #16 Jun 26 2024 04:25:42

%S 1,11,101,1011,10001,100111,1000001,10001011,100000101,1000010011,

%T 10000000001,100000101111,1000000000001,10000001000011,

%U 100000000010101,1000000010001011,10000000000000001,100000000100100111

%N a(n) = Sum_{ k, k|n } 10^(k-1).

%C A034729 to base 2. Stacking elements of the sequence gives A113998.

%H Seiichi Manyama, <a href="/A113999/b113999.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum_{n>0} x^n/(1-10*x^n).

%F a(n) ~ 10^(n-1). - _Vaclav Kotesovec_, Jun 05 2021

%t A113999[n_]:= DivisorSum[n, 10^(#-1) &];

%t Table[A113999[n], {n, 40}] (* _G. C. Greubel_, Jun 26 2024 *)

%o (PARI) a(n)=if(n<1,0,sumdiv(n,k,10^(k-1)));

%o (Magma)

%o A113999:= func< n | (&+[10^(d-1): d in Divisors(n)]) >;

%o [A113999(n): n in [1..40]]; // _G. C. Greubel_, Jun 26 2024

%o (SageMath)

%o def A113999(n): return sum(10^(k-1) for k in (1..n) if (k).divides(n))

%o [A113999(n) for n in range(1,41)] # _G. C. Greubel_, Jun 26 2024

%Y Sums of the form Sum_{d|n} q^(d-1): A034729 (q=2), A034730 (q=3), this sequence (q=10), A339684 (q=4), A339685 (q=5), A339686 (q=6), A339687 (q=7), A339688 (q=8), A339689 (q=9).

%K easy,nonn

%O 1,2

%A _Paul Barry_, Nov 12 2005