A348632 Nonexponential highly composite numbers: where the number of nonexponential divisors (A160097) increases to a record.

1, 6, 12, 24, 30, 60, 120, 210, 240, 360, 420, 720, 840, 1260, 1680, 2520, 3360, 5040, 7560, 9240, 10080, 15120, 18480, 25200, 27720, 36960, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 480480, 498960, 554400, 665280, 720720, 1081080, 1441440

Offset

1,2

Comments

The corresponding record values are 1, 3, 4, 6, 7, 10, 14, 15, 17, 20, 22, 24, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..651

Amiram Eldar, Table of n, a(n), A160097(a(n)) for n = 1..651

Mathematica

f1[p_, e_] := e + 1; f2[p_, e_] := DivisorSigma[0, e]; ned[1] = 1; ned[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) - Times @@ f2 @@@ f; dm = -1; s = {}; Do[If[(d = ned[n]) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s

Crossrefs

Cf. A160097.

Subsequence of A025487.

Similar sequences: A002182, A002110 (unitary), A037992 (infinitary), A293185, A306736, A307845, A309141, A318278, A322484, A335386.

Sequence in context: A216453 A119500 A260633 * A365470 A110967 A000082

Adjacent sequences: A348629 A348630 A348631 * A348633 A348634 A348635

Keyword

nonn

Author

Amiram Eldar, Oct 26 2021

Status

approved