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A327403
Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum stable divisor (A327393, A327402).
0
0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2
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. The maximum stable divisor of n is A327393(n).
EXAMPLE
We have 798 -> 42 -> 6 -> 2 -> 1, so a(798) = 4.
MATHEMATICA
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[FixedPointList[#/Max[Select[Divisors[#], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&]]&, n]]-2, {n, 100}]
CROSSREFS
See link for additional cross-references.
Positions of first appearance of each integer are A325782.
Sequence in context: A361631 A247462 A323172 * A247371 A331177 A173751
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 15 2019
STATUS
approved