A332043 Indices of records in A332042.

1, 6, 12, 24, 48, 72, 144, 288, 576, 864, 1152, 1440, 1728, 2160, 2304, 2880, 4320, 5760, 8640, 17280, 25920, 34560, 51840, 69120, 103680, 120960, 138240, 155520, 181440, 207360, 241920, 311040, 362880, 414720, 483840, 622080, 725760, 967680, 1244160, 1451520

Offset

1,2

Comments

Numbers k such that psi(x) = k has more solutions x than any smaller k, where psi(x) is the Dedekind psi function (A001615).

The corresponding number of solutions for each term is 1, 2, 4, 5, 6, 9, 11, 17, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..59

Amiram Eldar, Table of n, a(n), A332042(a(n)) for n = 1..59

Example

There are 2 solutions to psi(x) = 6: psi(4) = psi(5) = 6. For all m < 6 there are no more than one solution to psi(x) = m, thus 6 is in the sequence.

Mathematica

psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); m = 10000; v = Table[0, {m}]; Do[i = psi[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. A001615, A145899, A289132, A332037, A332039, A332041, A332042.

Sequence in context: A331200 A212116 A160728 * A362487 A229926 A082505

Adjacent sequences: A332040 A332041 A332042 * A332044 A332045 A332046

Keyword

nonn

Author

Amiram Eldar, Feb 05 2020

Status

approved