A301413 a(n) = A002182(n)/A002110(A108602(n)).

1, 1, 2, 1, 2, 4, 6, 8, 2, 4, 6, 8, 12, 24, 4, 6, 8, 12, 24, 36, 48, 72, 96, 120, 12, 216, 240, 24, 36, 48, 72, 96, 120, 144, 216, 240, 288, 24, 36, 48, 72, 96, 120, 144, 216, 240, 288, 360, 480, 576, 720, 1080, 72, 1440, 120, 144, 216, 240, 288, 360, 480, 576

Offset: 1

Author

Michael De Vlieger, Mar 30 2018

Keywords

• nonn

Comments

This sequence appears in Siano paper, page 5 of 12, as the "variable part" v. - Michael De Vlieger, Oct 11 2023

Examples

			Let m be a value in this sequence. The table below shows m*A002110(A108602(k)). Columns are A108602(k), rows are m whose products m*A002110(A108602(k)) appear in A002182 are in this sequence. Numbers in A002182 that also appear in A002201 are followed by (*).
        0  1   2    3     4       5       6 ...
      +------------------------------------
    1 | 1* 2*  6*
    2 |    4  12*  60*
    4 |       24  120*  840
    6 |       36  180  1260
    8 |       48  240  1680
   12 |           360* 2520*  27720
   24 |           720  5040*  55440* 720720*
   ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, On a graph of highly composite numbers
• A. Flammenkamp, Highly composite numbers
• D. B. Siano and J. D. Siano, An Algorithm for Generating Highly Composite Numbers, 1994.

Crossrefs

Cf. A002110, A002182, A108602, A301414.

Programs

Mathematica

(* Load b-file from A002182 *)
With[{s = Import["b002182.txt","Data"][[All,-1]]}, Array[#/Product[Prime@ i, {i, PrimeNu[#]}] &@ s[[#]] &, 62]]

Formula

a(n) = A002182(n)/A007947(A002182(n)).