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, 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).

Links

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

Gus Wiseman, Sequences counting and encoding certain classes of multisets

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.

Cf. A000005, A001222, A006530, A056239, A112798, A289509, A327407.

Sequence in context: A353756 A245690 A146291 * A346087 A086251 A177121

Adjacent sequences: A327535 A327536 A327537 * A327539 A327540 A327541

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved