A347356 a(n) = m/A006939(A001221(m)) with m = A347284(n).

1, 1, 2, 2, 2, 4, 24, 24, 48, 48, 96, 576, 576, 1152, 34560, 207360, 414720, 414720, 829440, 174182400, 1045094400, 2090188800, 2090188800, 2090188800, 4180377600, 25082265600, 25082265600, 50164531200, 1504935936000, 3009871872000, 18059231232000

Offset: 1

Author

Michael De Vlieger, Oct 02 2021

Keywords

• nonn

Examples

			Diagram of prime power decomposition of A347284(12) = 2^12 * 3^7 * 5^4 * 7^3 * 11^2 * 13, showing Chernoff number A006939(6) with "x" and "X", A002110(A347354(12)) with "X", and a(12) with "o":
          12  o
          11  o
          10  o
           9  o
           8  o
           7  o o
           6  x o
           5  x x
           4  x x x
           3  x x x x
           2  x x x x x
           1  X X X X X X
              2 3 5 7 ...
A347284(12) = A006939(6) * a(12)
          = 5244319080000 * 576
          = 3020727790080000.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..581
• Michael De Vlieger, Diagram of prime power decompositions of A347284(n) for 2 <= n <= 14, showing a(n) in blue, A006939(A089576(n)) in red, and the number A347284(n) in black.

Crossrefs

Cf. A001221, A006939, A089576, A347284.

Programs

Mathematica

Block[{nn = 31, a = {}, b, c, e, i, p}, Array[Set[e[#], 0] &, Floor[2^# If[# <= 4, 1/2, -1 + 2^(7/(3 #))]] &[Ceiling@ Log2@ nn]]; Do[e[1]++; b = {2^e[1]}; c = {e[1]}; Do[If[Last[b] == 1, Break[], i = e[j]; p = Prime[j]; While[p^i < b[[j - 1]], i++]; AppendTo[b, p^(i - 1)]; AppendTo[c, (i - 1)]; If[i > e[j], e[j]++]], {j, 2, k}]; AppendTo[a, If[First[#] == 0, 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, TakeWhile[#, # > 0 &]]] &[# - Range[Length[#], 1, -1]] &@ If[k > 2, Most@ c, c]], {k, nn}]; a]

Formula

a(n) = A347284(n)/A006939(A089576(n)).