A276651 a(n) = numerator of Sum_{p|n} 0.d where p runs through the prime divisors of n.

1, 3, 1, 1, 1, 7, 1, 3, 7, 11, 1, 13, 9, 4, 1, 17, 1, 19, 7, 1, 31, 23, 1, 1, 33, 3, 9, 29, 1, 31, 1, 41, 37, 6, 1, 37, 39, 43, 7, 41, 6, 43, 31, 4, 43, 47, 1, 7, 7, 47, 33, 53, 1, 61, 9, 49, 49, 59, 1, 61, 51, 1, 1, 63, 61, 67, 37, 53, 7, 71, 1, 73, 57, 4, 39

Offset: 2

Author

Jaroslav Krizek, Sep 10 2016

Keywords

• nonn
• base
• frac

Comments

Here 0.d means the decimal fraction obtained by writing d after the decimal point, e.g., 0.11 = 11/100.

The first few values of Sum_{p|n} 0.d are: 1/5, 3/10, 1/5, 1/2, 1/2, 7/10, 1/5, 3/10, 7/10, ...

See A276655 - numbers n such that Sum_{p|n} 0.d is an integer.

Examples

			For n=12; Sum_{p|12} 0.d = 0.2 + 0.3 = 0.5 = 5/10 = 1/2; a(12) = 1.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A276652, A276653, A276654, A276655, A276513.

Programs

Magma

[Numerator(&+[d/(10^(#Intseq(d))): d in PrimeDivisors(n)]): n in [2..1000]]

Mathematica

Numerator[Table[f = FactorInteger[i][[All, 1]];
Total[f*10^-IntegerLength[f]], {i, 2, 76}]] (* Robert Price, Sep 20 2019 *)

Formula

a(n) = (Sum_{p|n} 0.d) * A276652(n) where p = prime divisors of n.