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A276655
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Numbers j such that Sum_{p|j} 0.p is an integer where p ranges over the prime divisors of j.
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9
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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The prime divisors of 60 are 2, 3, and 5, and 0.2 + 0.3 + 0.5 = 1, so 60 is a term.
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MATHEMATICA
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{1}~Join~Select[Range[2400], IntegerQ@ Total[# 10^(-Floor@ Log10@ # - 1) &@ FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Sep 12 2016 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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