A332039 Indices of records in A332038.

1, 12, 24, 60, 120, 240, 360, 720, 1440, 2880, 4320, 5760, 7200, 8640, 11520, 14400, 17280, 21600, 25920, 28800, 34560, 43200, 60480, 86400, 120960, 129600, 172800, 241920, 259200, 302400, 345600, 483840, 518400, 604800, 907200, 1036800, 1209600, 1814400, 2419200

Offset

1,2

Comments

Numbers k such that isigma(x) = k has more solutions x than any smaller k, where isigma(x) is the sum of infinitary divisors of x (A049417).

The infinitary 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..53

Amiram Eldar, Table of n, a(n), A332038(a(n)) for n = 1..53

Example

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

Mathematica

fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 10000; v = Table[0, {m}]; Do[i = isigma[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

Crossrefs

Cf. A145899, A049417, A289132, A332037, A332038, A332041.

Sequence in context: A227895 A330076 A332037 * A001335 A206026 A145899

Adjacent sequences: A332036 A332037 A332038 * A332040 A332041 A332042

Keyword

nonn

Author

Amiram Eldar, Feb 05 2020

Status

approved