A391144 - OEIS

%I #9 Dec 01 2025 10:51:21

%S 4900,4150300,10716300,10765300,16240900,24073700,33609100,33988900,

%T 59618300,96446700,108784900,111724900,119506100,120780100,130188100,

%U 136656100,139948900,145975900,146652100,157000900,160528900,178756900,182520100,190164100,194044900,218152900

%N Primitive exponential weird numbers: powerful numbers that are exponential abundant (A129575) but not exponential pseudoperfect (A318100).

%C These are the primitive terms in A321146: Any term in A321146 is of the form k*m where k is a term in this sequence and m is a squarefree number coprime to k. Therefore, A321146 can be generated from this sequence by multiplying terms with coprime squarefree numbers, and the asymptotic density of A321146 can be evaluated from the terms in this sequence (see the Comments section of A321146).

%H Amiram Eldar, <a href="/A391144/b391144.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], eWeirdQ]; seq[5000] (* using the function "eWeirdQ" from A321146 *)

%Y Intersection of A001694 and A321146.

%Y Cf. A005117, A391143.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 01 2025