A327402 - OEIS

%I #12 Jan 28 2025 15:30:04

%S 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,

%T 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,

%U 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

%N Quotient of n over the maximum stable divisor of n.

%C 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.

%H Antti Karttunen, <a href="/A327402/b327402.txt">Table of n, a(n) for n = 1..20000</a>

%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

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

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

%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];

%t Table[n/Max[Select[Divisors[n],stableQ[PrimePi/@First/@FactorInteger[#],Divisible]&]],{n,100}]

%o (PARI)

%o 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

%o A327402(n) = fordiv(n,d,if(A378442(n/d),return(d))); \\ _Antti Karttunen_, Jan 28 2025

%Y See link for additional cross-references.

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

%K nonn

%O 1,6

%A _Gus Wiseman_, Sep 15 2019

%E Data section extended to a(105) by _Antti Karttunen_, Jan 28 2025