A332037 Indices of records in A332036.

1, 12, 24, 60, 120, 240, 360, 720, 1440, 2160, 2880, 4320, 5760, 7200, 8640, 12960, 14400, 17280, 21600, 25920, 28800, 30240, 34560, 40320, 43200, 51840, 60480, 86400, 120960, 172800, 181440, 241920, 259200, 302400, 362880, 483840, 518400, 604800, 725760, 907200

Offset

1,2

Comments

Numbers k such that bsigma(x) = k has more solutions x than any smaller k, where bsigma(x) is the sum of bi-unitary divisors of x (A188999).

The bi-unitary version of A145899.

The corresponding number of solutions for each term is 1, 2, 3, 5, 7, 12, 13, 20, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..58

Amiram Eldar, Table of n, a(n), A332036(a(n)) for n = 1..58

Example

There are 3 solutions to bsigma(x) = 24: bsigma(14) = bsigma(15) = bsigma(23) = 24. For all m < 24 there are 2 or fewer solutions to bsigma(x) = m, thus 24 is in the sequence.

Mathematica

fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 10000; v = Table[0, {m}]; Do[b = bsigma[k]; If[b <= m, v[[b]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

Crossrefs

Cf. A145899, A188999, A289132, A332036, A332037, A332039.

Sequence in context: A063975 A227895 A330076 * A332039 A001335 A206026

Adjacent sequences: A332034 A332035 A332036 * A332038 A332039 A332040

Keyword

nonn

Author

Amiram Eldar, Feb 05 2020

Status

approved