A327515 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, 2, or a nonprime number whose prime indices are pairwise coprime (A327512, A327514).

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0

Offset

1

Comments

Positions of zeros are A289509.

First term > 1 is a(225) = 2.

First zero not in A318978 is a(17719) = 0.

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 that are 1, 2, or a nonprime number whose prime indices are pairwise coprime are listed in A302696.

Links

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

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(15^n) = n.

Example

We have 50625 -> 3375 -> 225 ->  15 -> 1, so a(50625) = 4.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[FixedPointList[#/Max[Select[Divisors[#], #==1||CoprimeQ@@primeMS[#]&]]&, n]]-2, {n, 100}]

Crossrefs

See link for additional cross-references.

Cf. A000005, A006530, A056239, A112798, A289509, A302569, A302696, A304711.

Sequence in context: A188510 A131734 A134452 * A327532 A073445 A285589

Adjacent sequences: A327512 A327513 A327514 * A327516 A327517 A327518

Keyword

nonn

Author

Gus Wiseman, Sep 19 2019

Status

approved