OFFSET
1,3
COMMENTS
Ratio of A025487(n) and the largest primorial that divides A025487(n). The largest primorial that divides A025487(n) is A002110(A001221(n)).
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.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
EXAMPLE
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).
= 1 * 30
1 O O O
2 3 5
= 12 * 30
3 X
2 X X
1 O O O
2 3 5
= 72 * 2310
4 X
3 X X
2 X X
1 O O O O O
2 3 5 7 11
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]]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Michael De Vlieger, Mar 29 2019
STATUS
approved