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%I #30 Jan 23 2022 20:05:31
%S 1,21,30,60,63,90,120,147,150,180,189,240,270,300,360,441,450,480,540,
%T 567,600,720,750,810,900,960,979,1029,1080,1200,1323,1350,1411,1440,
%U 1463,1500,1547,1620,1701,1742,1800,1920,1947,2059,2090,2160,2210,2250,2318
%N Numbers j such that Sum_{p|j} 0.p is an integer where p ranges over the prime divisors of j.
%C Here 0.p means the decimal fraction obtained by writing p after the decimal point, e.g., 0.11 = 11/100.
%C 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, ...
%C 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.
%C See A276513 - the smallest number k such that Sum_{p|k} 0.p = n where p ranges over the prime divisors of k.
%C 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.
%C 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
%H Chai Wah Wu, <a href="/A276655/b276655.txt">Table of n, a(n) for n = 1..10000</a>
%F A276652(a(n)) = 1.
%e The prime divisors of 60 are 2, 3, and 5, and 0.2 + 0.3 + 0.5 = 1, so 60 is a term.
%t {1}~Join~Select[Range[2400], IntegerQ@ Total[# 10^(-Floor@ Log10@ # - 1) &@ FactorInteger[#][[All, 1]]] &] (* _Michael De Vlieger_, Sep 12 2016 *)
%o (Magma) [n: n in [1..1000000] | Denominator(&+[d/(10^(#Intseq(d))): d in PrimeDivisors(n)]) eq 1]
%o (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
%Y Cf. A276513, A276651, A276652, A276653, A276654.
%K nonn,base
%O 1,2
%A _Jaroslav Krizek_, Sep 10 2016
%E a(1) inserted by _Charles R Greathouse IV_, Sep 10 2016
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