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A327538
Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, prime, or whose prime indices are relatively prime (A327535, A327537).
0
0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2
OFFSET
1,9
COMMENTS
The first index m such that a(m) > 1 but m is not in A322336 is m = 2335.
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, prime, or whose prime indices are relatively prime are A327534. The number of divisors of n satisfying the same conditions is A327536(n).
FORMULA
a(1) = 0; if n is prime or has relatively prime prime indices, then a(n) = 1; otherwise a(n) = Omega(n) = A001222(n).
EXAMPLE
We have 441 -> 63 -> 9 -> 3 -> 1, so a(441) = 4.
MATHEMATICA
Table[Length[FixedPointList[#/Max[Select[Divisors[#], #==1||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]]&, n]]-2, {n, 100}]
CROSSREFS
See link for additional cross-references.
Sequence in context: A353756 A245690 A146291 * A346087 A086251 A374381
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2019
STATUS
approved