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

Author

Amiram Eldar, Feb 05 2020

Keywords

• nonn

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).

Examples

			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.
		

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

Crossrefs

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

Programs

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