A327402 Quotient of n over the maximum stable divisor of n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 5, 1, 6, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 7, 3, 2, 1, 4, 1, 2, 7, 1, 5, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 5, 1, 2, 1, 12, 1, 2, 3, 8, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 8, 3

Offset

1,6

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.

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) = n/A327393(n).

Example

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

Mathematica

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[n/Max[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
A327402(n) = fordiv(n, d, if(A378442(n/d), return(d))); \\ Antti Karttunen, Jan 28 2025

Crossrefs

See link for additional cross-references.

Cf. A000005, A033273, A303362, A316476, A327403, A378442.

Sequence in context: A340035 A185147 A206921 * A123529 A140747 A330757

Adjacent sequences: A327399 A327400 A327401 * A327403 A327404 A327405

Keyword

nonn

Author

Gus Wiseman, Sep 15 2019

Extensions

Data section extended to a(105) by Antti Karttunen, Jan 28 2025

Status

approved