A276466 a(n) = numerator of Sum_{d|n} 0.d.

1, 3, 2, 7, 3, 6, 4, 3, 13, 9, 21, 43, 23, 57, 21, 83, 27, 57, 29, 3, 131, 63, 33, 69, 17, 69, 157, 91, 39, 9, 41, 99, 21, 81, 33, 79, 47, 87, 23, 27, 51, 267, 53, 147, 12, 99, 57, 17, 129, 33, 27, 161, 63, 309, 63, 159, 29, 117, 69, 357, 71, 123, 71, 131, 69

Offset: 1

Author

Jaroslav Krizek, Sep 04 2016

Keywords

• nonn
• base

Comments

Let d be a divisor of n; 0.d means the decimal fraction formed 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 for n = 1,2,.. 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, ...

16450 is the only number < 5*10^7 such that Sum_{d|n} 0.d is an integer: Sum_{d | 16450} 0.d = 0.1 + 0.2 + 0.5 + 0.7 + 0.10 + 0.14 + 0.25 + 0.35 + 0.47 + 0.50 + 0.70 + 0.94 + 0.175 + 0.235 + 0.329 + 0.350 + 0.470 + 0.658 + 0.1175 + 0.1645 + 0.2350 + 0.3290 + 0.8225 + 0.16450 = 9; see A276465.

No other term like 16450 up to 4*10^11. - Giovanni Resta, Apr 03 2019

Examples

			For n=12; Sum_{d | 12} 0.d = 0.1 + 0.2 + 0.3 + 0.4 + 0.6 + 0.12 = 1.72 = 172/100 = 43/25; a(12) = 43.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A276465, A276467 (denominator).

Cf. A078267 and A078268 (both for 0.d).

Programs

Magma

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

Mathematica

Table[Numerator@ Total@ (#*1/10^(1 + Floor@ Log10@ #)) &@ Divisors@ n, {n, 65}] (* Michael De Vlieger, Sep 04 2016 *)

PARI

a(n) = numerator(sumdiv(n, d, d/10^(#Str(d)))); \\ Michel Marcus, Mar 29 2019

Python

from fractions import Fraction
from sympy import divisors
def A276466(n):
    return sum(Fraction(d,10**len(str(d))) for d in divisors(n)).numerator # Chai Wah Wu, Sep 05 2016

Formula

a(n) = (Sum_{d | n} 0.d) * A276467(n).