A391143 - OEIS

%I #9 Dec 01 2025 10:51:25

%S 36,900,1764,1800,2700,3600,4356,4500,6084,7056,8100,10404,12348,

%T 12996,17424,19044,22500,30276,34596,44100,47916,49284,60516,66564,

%U 79092,79524,86436,88200,101124,108900,112500,125316,132300,133956,152100,161604,176400,176868,181476,191844

%N Primitive exponential pseudoperfect numbers: powerful numbers equal to the sum of a subset of their proper exponential divisors.

%C These are the primitive terms in A318100: Any term in A318100 is of the form k*m where k is a term in this sequence and m is a squarefree number coprime to k. Therefore, A318100 can be generated from this sequence by multiplying terms with coprime squarefree numbers, and the asymptotic density of A318100 can be evaluated from the terms in this sequence (see the Comments section of A318100).

%C The least odd term is a(1690) = 225450225 = (3 * 5 * 7 * 11 * 13)^2.

%H Amiram Eldar, <a href="/A391143/b391143.txt">Table of n, a(n) for n = 1..10000</a>

%t pows[max_] := Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]];

%t seq[max_] := Select[pows[max], ePspQ]; seq[64000] (* using the function "ePspQ" from A318100 *)

%Y Intersection of A001694 and A318100.

%Y Cf. A005117, A391144.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 01 2025