A327659 Number of factorizations of A318978(n - 1), the n-th number that is 1 or whose prime indices have a common divisor > 1, into numbers > 1 satisfying the same conditions.

1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 4, 2, 1, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 4, 2, 3, 1, 2, 1, 2, 1, 1, 4, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 2, 2, 7, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 7, 2, 1, 1

Offset

1,5

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers whose prime indices have a common divisor > 1 are listed in A318978.

Links

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(n) = A001055(A318978(n - 1)).

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[1000], GCD@@PrimePi/@First/@FactorInteger[#]!=1&];
Table[Length[facsusing[Rest[y], n]], {n, y}]

Crossrefs

See link for additional cross-references.

Cf. A056239, A112798, A281116, A289509, A318721, A327406.

Sequence in context: A345238 A242442 A163768 * A327519 A287917 A325615

Adjacent sequences: A327656 A327657 A327658 * A327660 A327661 A327662

Keyword

nonn

Author

Gus Wiseman, Sep 21 2019

Status

approved