A327402 Quotient of n over the maximum stable divisor of n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 5, 1, 6, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 7, 3, 2, 1, 4, 1, 2, 7, 1, 5, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 5, 1, 2, 1, 12, 1, 2, 3

Offset

1,6

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. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476.

Links

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

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(n) = n/A327393(n).

Example

The stable divisors of 60 are {1, 2, 3, 4, 5, 15}, so a(60) = 60/15 = 4.

Mathematica

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[n/Max[Select[Divisors[n], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&]], {n, 100}]

Crossrefs

See link for additional cross-references.

Cf. A000005, A033273, A303362.

Sequence in context: A340035 A185147 A206921 * A123529 A140747 A330757

Adjacent sequences: A327399 A327400 A327401 * A327403 A327404 A327405

Keyword

nonn

Author

Gus Wiseman, Sep 15 2019

Status

approved