A327403 -id:A327403 - cp's OEIS frontend

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

Gus Wiseman, Sep 15 2019

nonn

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.

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

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.

See link for additional cross-references.

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

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}]

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

a(n) = n/A327393(n).

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

cp's OEIS Frontend

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

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