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

10, 10, 5, 10, 5, 5, 5, 2, 10, 10, 100, 25, 100, 50, 20, 50, 100, 25, 100, 2, 100, 100, 100, 25, 20, 100, 100, 50, 100, 4, 100, 50, 25, 100, 20, 25, 100, 100, 25, 10, 100, 100, 100, 100, 5, 100, 100, 5, 100, 20, 25, 100, 100, 100, 50, 50, 25, 100, 100, 100

Offset: 1

Author

Jaroslav Krizek, Sep 05 2016

Keywords

• base
• nonn

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 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, ...

a(16450) = 1: 16450 is the only integer < 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 10^9. - Michel Marcus, Mar 30 2019

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) = 25.
		

Crossrefs

Cf. A276465, A276466 (numerators).

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

Programs

Magma

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

Mathematica

Table[Denominator@ Total@ (#*1/10^(1 + Floor@ Log10@ #)) &@ Divisors@ n, {n, 60}] (* Michael De Vlieger, Sep 06 2016 *)

PARI

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

Formula

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