A289132 Indices of records in A063974.

1, 12, 24, 60, 72, 216, 240, 720, 1440, 2160, 2880, 4320, 8640, 10080, 12960, 17280, 20160, 25920, 30240, 40320, 43200, 51840, 60480, 90720, 103680, 120960, 181440, 241920, 302400, 362880, 483840, 604800, 725760, 1088640, 1209600, 1451520, 1814400, 2419200

Offset

1,2

Comments

Numbers n such that usigma(x) = n has more solutions x than any smaller n, where usigma(x) is the sum of unitary divisors of x (A034448).

The unitary version of A145899.

The corresponding number of solutions for each term is: 1, 2, 3, 4, 6, 7, 11, 18, 27, 30, 32, 48, 63, 65, 71, 88, 89, 102, 121, 122, 131, 144, 188, 190, 203, 262, 313, 364, 377, 472, 483, 584, 668, 725, 810, 928, 1076, 1138.

Is this a subsequence of A025487? - David A. Corneth, Jun 25 2017

Links

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

Example

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

Mathematica

usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[#, n/#] == 1 &]]; t = Map[usigma, Range[10^7]]; t2 = Sort[Tally[t]]; mn = 0; t3 = {}; Do[If[t2[[n]][[2]] > mn, mn = t2[[n]][[2]]; AppendTo[t3, t2[[n]][[1]]]], {n, Length[t2]}]; t3 (* after T. D. Noe at A145899 *)

Crossrefs

Cf. A025487, A034448, A063974, A145899.

Sequence in context: A346865 A123980 A097704 * A348716 A098585 A087105

Adjacent sequences: A289129 A289130 A289131 * A289133 A289134 A289135

Keyword

nonn

Author

Amiram Eldar, Jun 25 2017

Status

approved