A307107 a(n) = A025487(n)/A247451(n).

1, 1, 2, 1, 4, 2, 8, 4, 1, 16, 6, 8, 2, 32, 12, 16, 4, 64, 24, 6, 32, 1, 36, 8, 128, 48, 12, 64, 2, 72, 16, 256, 96, 24, 128, 4, 144, 30, 32, 512, 36, 192, 6, 216, 48, 256, 8, 288, 60, 64, 1024, 72, 384, 1, 12, 432, 96, 512, 16, 576, 120, 128, 2048, 144, 768, 2

Offset: 1

Author

Michael De Vlieger, Mar 29 2019

Keywords

• nonn
• look

Comments

Ratio of A025487(n) and the largest primorial that divides A025487(n). The largest primorial that divides A025487(n) is A002110(A001221(n)).

If A025487(n) is a primorial (i.e., in A002110), a(n) = 1.

a(n) is in A025487 by definition of that sequence as a sorted list of products of primorials.

Conjectures:

1. 1 is the most common value in this sequence even though it only pertains to primorials.

2. All terms in A025487 are in this sequence.

Examples

			We can represent the prime divisors p with multiplicity of A025487(n) in a chart where the columns pertain to p and the rows multiplicity. In such a chart, A247451(n) is the longest row (marked by "O" below), and a(n) is the product of primes left over (marked by "X") when we eliminate the primes that produce A247451(n).
A025487(9) =       30 = a(9) * A247451(9)
                      = 1 * 30
  1  O O O
     2 3 5
A025487(27) =     360 = a(27) * A247451(27)
                      = 12 * 30
  3  X
  2  X X
  1  O O O
     2 3 5
A025487(183) = 166320 = a(183) * A247451(183)
                      = 72 * 2310
  4  X
  3  X X
  2  X X
  1  O O O O O
     2 3 5 7 11
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A002110, A025487, A061394, A247451.

Programs

Mathematica

f[n_] := {{1}}~Join~Block[{lim = Product[Prime@ i, {i, n}], ww = NestList[Append[#, 1] &, {1}, n - 1], g}, g[x_] := Apply[Times, MapIndexed[Prime[First@ #2]^#1 &, x]]; Map[Block[{w = #, k = 1}, Sort@ Prepend[If[Length@ # == 0, #, #[[1]]], Product[Prime@ i, {i, Length@ w}]] &@ Reap[Do[If[# < lim, Sow[#]; k = 1, If[k >= Length@ w, Break[], k++]] &@ g@ Set[w, If[k == 1, MapAt[# + 1 &, w, k], PadLeft[#, Length@ w, First@#] &@ Drop[MapAt[# + Boole[i > 1] &, w, k], k - 1]]], {i, Infinity}]][[-1]]] &, ww]]; With[{s = Union@ Flatten@ f@ 6}, Map[#/Product[Prime@ i, {i, PrimeNu@ #}] &, s]]

Formula

a(n) = A025487(n)/A002110(A061394(n)) = A025487(n)/A002110(A001221(A025487(n))).