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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 15:42 EDT 2020. Contains 337310 sequences. (Running on oeis4.)