cp's OEIS Frontend

A327537 Quotient of n over the maximum divisor of n that is 1, prime, or whose prime indices are relatively prime.

%I A327537 #4 Sep 18 2019 04:58:14
%S A327537 1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,5,1,9,1,1,1,1,1,1,1,
%T A327537 1,1,1,1,3,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,3,1,1,1,1,1,9,1,5,1,1,1,
%U A327537 1,1,1,1,1,1,1,1,1,1,1,1,27,1,1,1,1,1,3
%N A327537 Quotient of n over the maximum divisor of n that is 1, prime, or whose prime indices are relatively prime.
%C A327537 All terms are odd.
%C A327537 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 that are 1, prime, or whose prime indices are relatively prime are A327534. The maximum divisor of n satisfying the same conditions is A327535(n).
%H A327537 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%F A327537 If n is in A327534, then a(n) = 1; otherwise a(n) = n/A006530(n) = A032742(n).
%e A327537 The divisors of 63 that are 1, prime, or whose prime indices are relatively prime are {1, 3, 7}, so a(63) = 63/7 = 9.
%t A327537 Table[n/Max[Select[Divisors[n],#==1||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]],{n,100}]
%Y A327537 See link for additional cross-references.
%Y A327537 Cf. A000005, A006530, A032742, A056239, A112798, A289509, A327407.
%K A327537 nonn
%O A327537 1,9
%A A327537 _Gus Wiseman_, Sep 17 2019