OFFSET
1,2
COMMENTS
Here 0.p means the decimal fraction obtained by writing p after the decimal point, e.g., 0.11 = 11/100.
The first few values of Sum_{p|n} 0.p for n >= 1 are 0, 1/5, 3/10, 1/5, 1/2, 1/2, 7/10, 1/5, 3/10, 7/10, ...
Numbers j such that Sum_{p|j} 0.p (where p ranges over the prime divisors of j) = numbers j such that A276651(j) / A276652(j) is an integer.
See A276513 - the smallest number k such that Sum_{p|k} 0.p = n where p ranges over the prime divisors of k.
Sum_{p|a(n)} 0.p = 1 for first 133 terms of this sequence; Sum_{p|a(134)} 0.p = Sum_{p|16102} 0.p = 2. For number 16102 with set of prime divisors {2, 83, 97} holds: 0.2 + 0.83 + 0.97 = 2.
It is clear from the definition that if j is in the sequence so are all numbers m with rad(m) = rad(j). For example, since 21 is in the sequence, so are 63, 147, 189, 441, 567, 1029, 1323, 1701, etc. - Charles R Greathouse IV, Sep 10 2016
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
FORMULA
A276652(a(n)) = 1.
EXAMPLE
The prime divisors of 60 are 2, 3, and 5, and 0.2 + 0.3 + 0.5 = 1, so 60 is a term.
MATHEMATICA
{1}~Join~Select[Range[2400], IntegerQ@ Total[# 10^(-Floor@ Log10@ # - 1) &@ FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Sep 12 2016 *)
PROG
(Magma) [n: n in [1..1000000] | Denominator(&+[d/(10^(#Intseq(d))): d in PrimeDivisors(n)]) eq 1]
(PARI) is(n)=my(f=factor(n)[, 1]); denominator(sum(i=1, #f, f[i]/10^#Str(f[i])))==1 \\ Charles R Greathouse IV, Sep 10 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Sep 10 2016
EXTENSIONS
a(1) inserted by Charles R Greathouse IV, Sep 10 2016
STATUS
approved