A276479 a(n) = floor(Sum_{d|n} 0.d).

0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 1, 3, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 3, 1, 1, 1, 1, 0, 3, 1, 3, 1, 1, 0, 3, 0, 1, 2, 2, 1, 2, 0, 1, 1, 2, 0, 4, 0, 1, 2, 2, 1, 2, 0, 3, 2, 1, 0, 4, 1, 1, 1

Offset: 1

Author

Jaroslav Krizek, Sep 05 2016

Keywords

• nonn
• base

Comments

Here 0.d means the decimal fraction obtained by writing d after the decimal point, e.g. 0.12 = 12/100 = 3/25.

The first few values of Sum_{d|n} 0.d are: 1/10, 3/10, 2/5, 7/10, 3/5, 6/5, 4/5, 3/2, 13/10, 9/10, 21/100, 43/25, ...

See A276480(n) = the smallest number k such that floor(Sum_{d|k} 0.d) = n.

Examples

			For n=12: a(12) = floor(Sum_{d|12} 0.d) = floor(0.1 + 0.2 + 0.3 + 0.4 + 0.6 + 0.12 = 0.72) = floor(172/100) = floor(43/25)  = 1.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A276466, A276467, A276480.

Programs

Magma

[Floor(&+[d / (10^(#Intseq(d))): d in Divisors(n)]): n in [1..1000]];

Mathematica

Table[Floor@ Total@ (#*1/10^(1 + Floor@ Log10@ #)) &@ Divisors@ n, {n, 120}] (* Michael De Vlieger, Sep 06 2016 *)

PARI

a(n) = floor(sumdiv(n, d, d/10^(#Str(d)))); \\ Michel Marcus, Sep 05 2016

Python

from fractions import Fraction
from sympy import divisors
def A276479(n):
    return sum(Fraction(d,10**len(str(d))) for d in divisors(n))._floor_() # Chai Wah Wu, Sep 08 2016

Formula

a(n) = floor(A276466(n)/A276467(n)).