cp's OEIS Frontend

A327405 Quotient of n over the maximum divisor of n that is 1 or whose prime indices have a common divisor > 1.

%I A327405 #13 Dec 06 2021 10:57:01
%S A327405 1,2,1,4,1,2,1,8,1,2,1,4,1,2,3,16,1,2,1,4,1,2,1,8,1,2,1,4,1,6,1,32,3,
%T A327405 2,5,4,1,2,1,8,1,2,1,4,5,2,1,16,1,2,3,4,1,2,5,8,1,2,1,12,1,2,1,64,1,6,
%U A327405 1,4,3,10,1,8,1,2,3,4,7,2,1,16,1,2,1,4,5
%N A327405 Quotient of n over the maximum divisor of n that is 1 or whose prime indices have a common divisor > 1.
%C A327405 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. Numbers whose prime indices have a common divisor > 1 are listed in A318978.
%H A327405 Antti Karttunen, <a href="/A327405/b327405.txt">Table of n, a(n) for n = 1..20000</a>
%H A327405 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 A327405 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A327405 a(n) = n/A327656(n).
%e A327405 The divisors of 90 that are 1 or whose prime indices have a common divisor > 1 are {1, 3, 5, 9}, so a(90) = 90/9 = 10.
%t A327405 Table[n/Max[Select[Divisors[n],GCD@@PrimePi/@First/@FactorInteger[#]!=1&]],{n,100}]
%o A327405 (PARI) A327405(n) = (n / vecmax(select(d -> (1==d)||(gcd(apply(primepi,factor(d)[, 1]~))>1), divisors(n)))); \\ _Antti Karttunen_, Dec 06 2021
%Y A327405 See link for additional cross-references.
%Y A327405 Cf. A000005, A056239, A112798, A281116, A289509, A302569.
%K A327405 nonn,look
%O A327405 1,2
%A A327405 _Gus Wiseman_, Sep 21 2019