cp's OEIS Frontend

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

%I A327402 #12 Jan 28 2025 15:30:04
%S A327402 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 A327402 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 A327402 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 A327402 Quotient of n over the maximum stable divisor of n.
%C A327402 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 A327402 Antti Karttunen, <a href="/A327402/b327402.txt">Table of n, a(n) for n = 1..20000</a>
%H A327402 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 A327402 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%F A327402 a(n) = n/A327393(n).
%e A327402 The stable divisors of 60 are {1, 2, 3, 4, 5, 15}, so a(60) = 60/15 = 4.
%t A327402 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A327402 Table[n/Max[Select[Divisors[n],stableQ[PrimePi/@First/@FactorInteger[#],Divisible]&]],{n,100}]
%o A327402 (PARI)
%o A327402 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 A327402(n) = fordiv(n,d,if(A378442(n/d),return(d))); \\ _Antti Karttunen_, Jan 28 2025
%Y A327402 See link for additional cross-references.
%Y A327402 Cf. A000005, A033273, A303362, A316476, A327403, A378442.
%K A327402 nonn
%O A327402 1,6
%A A327402 _Gus Wiseman_, Sep 15 2019
%E A327402 Data section extended to a(105) by _Antti Karttunen_, Jan 28 2025