A327518 Number of factorizations of A302696(n), the n-th number that is 1, 2, or a nonprime number with pairwise coprime prime indices, into factors > 1 satisfying the same conditions.

1, 1, 2, 1, 3, 1, 2, 1, 1, 5, 2, 1, 4, 1, 2, 2, 7, 1, 1, 1, 1, 4, 2, 1, 7, 1, 2, 1, 4, 1, 5, 1, 11, 2, 2, 1, 2, 1, 2, 1, 7, 1, 1, 1, 4, 2, 1, 1, 1, 12, 2, 4, 1, 2, 7, 2, 1, 1, 10, 1, 1, 2, 15, 5, 1, 4, 2, 5, 1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 12, 1, 2, 1, 1, 2, 2

Offset

1,3

Links

Table of n, a(n) for n=1..85.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Example

The a(59) = 10 factorizations of 120 using the allowed factors, together with the corresponding multiset partitions of {1,1,1,2,3}:
  (2*2*2*15)  {{1},{1},{1},{2,3}}
  (2*2*30)    {{1},{1},{1,2,3}}
  (2*4*15)    {{1},{1,1},{2,3}}
  (2*6*10)    {{1},{1,2},{1,3}}
  (2*60)      {{1},{1,1,2,3}}
  (4*30)      {{1,1},{1,2,3}}
  (6*20)      {{1,2},{1,1,3}}
  (8*15)      {{1,1,1},{2,3}}
  (10*12)     {{1,3},{1,1,2}}
  (120)       {{1,1,1,2,3}}

Mathematica

nn=100;
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
y=Select[Range[nn], #==1||CoprimeQ@@primeMS[#]&];
Table[Length[facsusing[Rest[y], n]], {n, y}]

Crossrefs

See link for additional cross-references.

Cf. A001055, A056239, A112798, A302569, A302696, A304711, A305079, A327392.

Sequence in context: A366833 A353161 A327533 * A174532 A089242 A349258

Adjacent sequences: A327515 A327516 A327517 * A327519 A327520 A327521

Keyword

nonn

Author

Gus Wiseman, Sep 19 2019

Status

approved