A327394 Number of stable divisors of n.

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, 5, 2, 7, 4, 4, 4, 3, 4, 7, 2, 4, 6, 5, 2, 5, 2, 5, 6, 3, 2, 6, 2, 5, 3, 6, 2, 4, 3, 4, 4, 3, 4, 7, 3

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

Antti Karttunen, Table of n, a(n) for n = 1..20000

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Index entries for sequences related to prime indices in the factorization of n

Formula

a(n) = Sum_{d|n} A378442(d). - Antti Karttunen, Nov 27 2024

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}]

Prog

(PARI)
A378442(n)={my(v=apply(primepi, factor(n)[, 1])); for(j=2, #v, for(i=1, j-1, if(v[j]%v[i]==0, return(0)))); 1}; \\ From the function "ok" in A316476 by Andrew Howroyd, Aug 26 2018
A327394(n) = sumdiv(n, d, A378442(d)); \\ Antti Karttunen, Nov 27 2024

Crossrefs

See link for additional cross-references.

Cf. A000005, A033273, A303362, A316476, A327393.

Inverse Möbius transform of A378442.

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

Extensions

More terms from Antti Karttunen, Nov 27 2024

Status

approved