A343014 Number with a record number of divisors whose prime factorizations contain no repeated exponents.

1, 2, 4, 8, 12, 24, 48, 72, 96, 144, 288, 432, 576, 720, 864, 1152, 1440, 2160, 2880, 4320, 5760, 8640, 12960, 17280, 25920, 34560, 43200, 51840, 69120, 77760, 86400, 103680, 129600, 155520, 172800, 207360, 259200, 345600, 388800, 518400, 777600, 907200, 1036800

Offset

1,2

Comments

Indices of records of A181796.

Since A181796(n) depends only on the prime signature of n, this sequence is a subsequence of A025487.

The corresponding record values are 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, ... (see the link for more values).

From David A. Corneth, Apr 04 2021: (Start)

Subsequence of A087980 and of A181824.

Let G_m be the gcd of terms k with omega(k) = m. So G_1 <= 2, G_2 <= 12, G_3 <= 720, G_4 <= 907200.

Do we have G_m | G_(m + 1)? (End)

Links

David A. Corneth, Table of n, a(n) for n = 1..700 (first 500 terms from Amiram Eldar)

Amiram Eldar, Table of n, a(n), A181796(a(n)) for n = 1..500

Example

A181796 begins with 1, 2, 2, 3, 2, 3, 2, 4, .... The record values, 1, 2, 3 and 4 occur at 1, 2, 4 and 8, which are the first 4 terms of this sequence.

Mathematica

q[n_] := UnsameQ @@ FactorInteger[n][[;; , 2]]; s[n_] := DivisorSum[n, 1 &, q[#] &]; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^4}]; seq

Crossrefs

Cf. A025487, A087980, A130091, A181796, A181824.

Sequence in context: A279312 A326076 A181808 * A097942 A354541 A358513

Adjacent sequences: A343011 A343012 A343013 * A343015 A343016 A343017

Keyword

nonn

Author

Amiram Eldar, Apr 02 2021

Status

approved