A113999 a(n) = Sum_{ k, k|n } 10^(k-1).

1, 11, 101, 1011, 10001, 100111, 1000001, 10001011, 100000101, 1000010011, 10000000001, 100000101111, 1000000000001, 10000001000011, 100000000010101, 1000000010001011, 10000000000000001, 100000000100100111

Offset: 1

Author

Paul Barry, Nov 12 2005

Keywords

• easy
• nonn

Comments

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

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).

Programs

Magma

A113999:= func< n | (&+[10^(d-1): d in Divisors(n)]) >;
[A113999(n): n in [1..40]]; // G. C. Greubel, Jun 26 2024

Mathematica

A113999[n_]:= DivisorSum[n, 10^(#-1) &];
Table[A113999[n], {n, 40}] (* G. C. Greubel, Jun 26 2024 *)

PARI

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

SageMath

def A113999(n): return sum(10^(k-1) for k in (1..n) if (k).divides(n))
[A113999(n) for n in range(1,41)] # G. C. Greubel, Jun 26 2024

Formula

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

a(n) ~ 10^(n-1). - Vaclav Kotesovec, Jun 05 2021