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A297358
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Numbers m such that the denominator of m/rho(m) is 3, where rho is A206369; i.e. A294649(m) = 3.
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0
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4, 14, 20, 84, 280, 672, 3360, 4200, 4214, 6160, 25284, 36960, 46200, 57792, 76160, 84280, 92400, 202272, 288960, 308700, 656640, 1011360, 1142400, 1264200, 1854160, 2469600, 3178560, 11124960, 12566400, 13906200, 22924160, 27812400, 107557632, 120165120, 212385600
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OFFSET
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1,1
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COMMENTS
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The least instances for 4/3, 5/3, 7/3, 8/3, 10/3 and 11/3 are: 4, 20, 14, 672, 3360, 36960.
Then candidates for 13/3 and 14/3 are 54269201896764616671660406473798293913600000 and 23101697828019582727957348094429256309828763084415991060514234912131560924774400000000.
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LINKS
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EXAMPLE
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4 is a term because 4/A206369(4) = 4/3.
14 is a term because 14/A206369(14) = 14/6 = 7/3.
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MATHEMATICA
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Select[Range[10^5], Denominator[#/(# DivisorSum[#, LiouvilleLambda[#]/# &])] == 3 &] (* Michael De Vlieger, Dec 29 2017 *)
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PROG
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(PARI) rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
isok(n) = denominator(n/rho(n))==3;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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