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A276655 Numbers n such that Sum_{p|n} 0.p is an integer where p ranges over the prime divisors of n. 9
1, 21, 30, 60, 63, 90, 120, 147, 150, 180, 189, 240, 270, 300, 360, 441, 450, 480, 540, 567, 600, 720, 750, 810, 900, 960, 979, 1029, 1080, 1200, 1323, 1350, 1411, 1440, 1463, 1500, 1547, 1620, 1701, 1742, 1800, 1920, 1947, 2059, 2090, 2160, 2210, 2250, 2318 (list; graph; refs; listen; history; text; internal format)
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 are: 1/5, 3/10, 1/5, 1/2, 1/2, 7/10, 1/5, 3/10, 7/10, ...

Numbers n such that Sum_{p|n} 0.p (where p ranges over the prime divisors of n) = A276651(n) / A276652(n) 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 n is in the sequence so are all numbers m with rad(m) = rad(n). 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

Number 60 with set of prime divisors {2, 3, 5} is in the sequence because 0.2 + 0.3 + 0.5 = 1.

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

Cf. A276513, A276651, A276652, A276653, A276654.

Sequence in context: A308339 A186455 A318081 * A187965 A318349 A228142

Adjacent sequences:  A276652 A276653 A276654 * A276656 A276657 A276658

KEYWORD

nonn,base

AUTHOR

Jaroslav Krizek, Sep 10 2016

EXTENSIONS

a(1) inserted by Charles R Greathouse IV, Sep 10 2016

STATUS

approved

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)