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A276513
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a(n) = the smallest number k>1 such that Sum_{p|k} 0.p = n where p runs through the prime divisors of k.
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6
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OFFSET
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1,1
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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.
a(n) = the smallest number k>1 such that A276651(k) / A276652(k) = n.
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, ...
Conjecture: a(4) = 730610790; Sum_{p|730610790} 0.p = 0.2 + 0.3 + 0.5 + 0.7 + 0.13 + 0.31 + 0.89 + 0.97 = 4.
Subsequence of A005117. - Chai Wah Wu, Sep 15 2016
a(8) <= 8646420251472669505, a(9) <= 1879755659507289195345, a(10) <= 3625424828481802325595910. - Giovanni Resta, Aug 19 2019
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LINKS
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Table of n, a(n) for n=1..7.
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EXAMPLE
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Number 16102 is the smallest number k with Sum_{p|k} 0.p = 2; set of prime divisors of 16102: {2, 83, 97}; Sum_{p|16102} 0.p = 0.2 + 0.83 + 0.97 = 2.
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MATHEMATICA
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Table[k = 1;
While[f = FactorInteger[k][[All, 1]];
Total[f*10^-IntegerLength[f]] != n, k++];
k, {n, 1, 4}] (* Robert Price, Sep 20 2019 *)
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PROG
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(MAGMA) A276513:=func<n|exists(r){k:k in[2..10^6] | (&+[d / (10^(#Intseq(d))): d in PrimeDivisors(k)]) eq n}select r else 0>; [A276513(n): n in[1..3]]
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CROSSREFS
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Cf. A005117, A276651, A276652, A276653, A276654, A276655.
Sequence in context: A180769 A220643 A185557 * A167063 A115485 A172724
Adjacent sequences: A276510 A276511 A276512 * A276514 A276515 A276516
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KEYWORD
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nonn,base,more
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AUTHOR
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Jaroslav Krizek, Sep 14 2016
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EXTENSIONS
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a(4) from Chai Wah Wu, Sep 16 2016
a(5)-a(7) from Giovanni Resta, Aug 19 2019
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STATUS
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approved
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