

A327394


Number of stable divisors of n.


0



1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 4, 5, 2, 4, 2, 4, 3, 3, 2, 5, 3, 3, 4, 4, 2, 5, 2, 6, 4, 3, 4, 5, 2, 3, 3, 5, 2, 4, 2, 4, 6, 3, 2, 6, 3, 4, 4, 4, 2, 5, 4, 5, 3, 3, 2, 6, 2, 3, 4, 7, 3, 5, 2, 4, 4, 5, 2, 6, 2, 3, 6, 4, 4, 4, 2, 6, 5, 3, 2, 5, 4, 3, 3
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OFFSET

1,2


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. Maximum stable divisor is A327393.


LINKS

Table of n, a(n) for n=1..87.
Gus Wiseman, Sequences counting and encoding certain classes of multisets


EXAMPLE

The stable divisors of 60 are {1, 2, 3, 4, 5, 15}, so a(60) = 6.


MATHEMATICA

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[Divisors[n], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&]], {n, 100}]


CROSSREFS

See link for additional crossreferences.
Cf. A000005, A033273, A303362.
Sequence in context: A073093 A326196 A222084 * A088873 A085082 A335516
Adjacent sequences: A327391 A327392 A327393 * A327395 A327396 A327397


KEYWORD

nonn


AUTHOR

Gus Wiseman, Sep 15 2019


STATUS

approved



