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A383360 Numbers k that have an i-th smallest divisor d_i(k) for which i*d_i(k) = k.

%I A383360 #13 May 02 2025 19:33:44
%S A383360 1,4,15,20,21,27,28,30,32,33,39,40,44,48,51,52,57,68,69,76,84,87,92,
%T A383360 93,111,112,116,123,124,129,141,144,148,159,160,164,172,175,177,183,
%U A383360 188,200,201,210,212,213,219,224,236,237,240,244,245,249,267,268,270,275
%N A383360 Numbers k that have an i-th smallest divisor d_i(k) for which i*d_i(k) = k.
%C A383360 Numbers k for which a number i exists such that k = i*A027750(k,i).
%H A383360 Felix Huber, <a href="/A383360/b383360.txt">Table of n, a(n) for n = 1..10000</a>
%H A383360 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Divisor.html">Divisor</a>.
%F A383360 a(n) = A383362(n)*A383361(n).
%F A383360 a(n) = A383362(n)*A027750(a(n),A383362(n)).
%e A383360 30 is in the sequence because its 5th smallest divisor is 6 and 5*6 = 30.
%p A383360 with(NumberTheory):
%p A383360 A383360:=proc(n)
%p A383360     option remember;
%p A383360     local k,i,L;
%p A383360     if n=1 then
%p A383360         1
%p A383360     else
%p A383360         for k from procname(n-1)+1 do
%p A383360             L:=Divisors(k);
%p A383360             for i to tau(k) do
%p A383360                 if L[i]*i=k then
%p A383360                     return k
%p A383360                 fi
%p A383360             od
%p A383360         od
%p A383360     fi;
%p A383360 end proc;
%p A383360 seq(A383360(n),n=1..58);
%t A383360 q[k_] := AnyTrue[(d = Divisors[k]) * Range[Length[d]], # == k &]; Select[Range[300], q] (* _Amiram Eldar_, Apr 26 2025 *)
%o A383360 (PARI) isok(k) = my(d=divisors(k)); for (i=1, #d, if (d[i]*i == k, return(1))); \\ _Michel Marcus_, Apr 26 2025
%Y A383360 Cf. A027750, A383361, A383362.
%K A383360 nonn,easy
%O A383360 1,2
%A A383360 _Felix Huber_, Apr 26 2025