A361319 Indices of records in the sequence of infinitary harmonic means A361316(k)/A361317(k).

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 54, 56, 60, 84, 105, 120, 168, 210, 264, 270, 280, 360, 420, 540, 660, 756, 840, 1080, 1320, 1512, 1848, 1890, 2310, 2520, 3080, 3640, 3780, 4620, 5460, 5940, 7020, 7560, 9240, 10920, 11880, 14040, 16632, 19656

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..200

Example

The infinitary harmonic means of the first 6 positive integers are 1 < 4/3 < 3/2 < 8/5 < 5/3 < 2. The next record, A361316(8)/A361317(8) = 32/15, occurs at 8. Therefore, the first 7 terms of this sequence are 1, 2, 3, 4, 5, 6 and 8.

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 2/(1 + p^(2^(m - j))), 1], {j, 1, m}]]; ihmean[1] = 1; ihmean[n_] := n*Times @@ f @@@ FactorInteger[n]; seq[kmax_] := Module[{ih, ihmax = 0, s = {}}, Do[ih = ihmean[k]; If[ih > ihmax, ihmax = ih; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[20000]

Prog

(PARI) ihmean(n) = {my(f = factor(n), b); n * prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 2/(f[i, 1]^(2^(#b-k))+1), 1))); };
lista(kmax) = {my(ih, ihmax=0); for(k = 1, kmax, ih = ihmean(k); if(ih > ihmax, ihmax = ih; print1(k, ", "))); }

Crossrefs

Cf. A361316, A361317.

Similar sequences: A179971, A348654.

Other sequences related to records of infinitary divisors: A037992, A327634.

Sequence in context: A279077 A018541 A361785 * A018293 A015702 A362127

Adjacent sequences: A361316 A361317 A361318 * A361320 A361321 A361322

Keyword

nonn

Author

Amiram Eldar, Mar 09 2023

Status

approved