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A361785
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Indices of records in the sequence of bi-unitary harmonic means A361782(k)/A361783(k).
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1
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1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 54, 56, 60, 84, 96, 120, 168, 210, 240, 270, 280, 360, 420, 480, 672, 840, 1080, 1320, 1512, 1680, 1890, 2160, 2310, 2520, 3080, 3360, 4320, 5280, 6048, 7392, 7560, 9240, 10920, 11880, 14040, 15120, 18480, 20790
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The harmonic means of the bi-unitary divisors of the first 6 positive integers are 1 < 4/3 < 3/2 < 8/5 < 5/3 < 2. A361782(7)/A361783(7) = 9/5 < 2, and the next record, A361782(8)/A361783(8) = 32/15, occurs at 8. Therefore, the first 7 terms of this sequence are 1, 2, 3, 4, 5, 6 and 8.
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MATHEMATICA
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f[p_, e_] := p^e * If[OddQ[e], (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2))]; buhmean[1] = 1; buhmean[n_] := Times @@ f @@@ FactorInteger[n]; seq[kmax_] := Module[{buh, buhmax = 0, s = {}}, Do[buh = buhmean[k]; If[buh > buhmax, buhmax = buh; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[20000]
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PROG
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(PARI) buhmean(n) = {my(f = factor(n), p, e); n * prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; if(e%2, (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2)))); }
lista(kmax) = {my(buh, buhmax=0); for(k = 1, kmax, buh = buhmean(k); if(buh > buhmax, buhmax = buh; print1(k, ", "))); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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