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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 (list; graph; refs; listen; history; text; internal format)
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 cross-references.

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

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Last modified August 3 04:47 EDT 2021. Contains 346435 sequences. (Running on oeis4.)