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A383362 a(n) is the number i for which i*d_i = A383360(n), where d_i is i-th smallest divisor d_i of A383360(n).

%I A383362 #5 May 08 2025 18:09:01
%S A383362 1,2,3,4,3,3,4,5,4,3,3,5,4,6,3,4,3,4,3,4,7,3,4,3,3,7,4,3,4,3,3,9,4,3,
%T A383362 8,4,4,5,3,3,4,8,3,10,4,3,3,8,4,3,12,4,5,3,3,4,10,5,10,4,3,4,3,3,4,3,
%U A383362 5,3,4,3,4,3,4,8,3,10,4,3,4,3,5,4,4,7,3,4
%N A383362 a(n) is the number i for which i*d_i = A383360(n), where d_i is i-th smallest divisor d_i of A383360(n).
%H A383362 Felix Huber, <a href="/A383362/b383362.txt">Table of n, a(n) for n = 1..10000</a>
%F A383362 a(n) = A383360(n)/A383361(n).
%F A383362 a(n) = A383360(n)/A027750(A383360(n),a(n)).
%e A383362 a(8) = 5 because the 5th smallest divisor of A383360(8) = 30 = 5*6 is 6.
%p A383362 with(NumberTheory):
%p A383362 A383360:=proc(n)
%p A383362     option remember;
%p A383362     local k,i,L;
%p A383362     if n=1 then
%p A383362         1
%p A383362     else
%p A383362         for k from procname(n-1)+1 do
%p A383362             L:=Divisors(k);
%p A383362             for i to tau(k) do
%p A383362                 if L[i]*i=k then
%p A383362                     return k
%p A383362                 fi
%p A383362             od
%p A383362         od
%p A383362     fi;
%p A383362 end proc;
%p A383362 A383362:=proc(n)
%p A383362     local i,M;
%p A383362     M:=Divisors(A383360(n));
%p A383362     for i do
%p A383362         if A383360(n)/i=M[i] then
%p A383362             return i
%p A383362         fi
%p A383362     od;
%p A383362 end proc;
%p A383362 seq(A383360(n),n=1..86);
%Y A383362 Cf. A383360, A383361.
%K A383362 nonn,easy
%O A383362 1,2
%A A383362 _Felix Huber_, May 03 2025