A391144 Primitive exponential weird numbers: powerful numbers that are exponential abundant (A129575) but not exponential pseudoperfect (A318100).

4900, 4150300, 10716300, 10765300, 16240900, 24073700, 33609100, 33988900, 59618300, 96446700, 108784900, 111724900, 119506100, 120780100, 130188100, 136656100, 139948900, 145975900, 146652100, 157000900, 160528900, 178756900, 182520100, 190164100, 194044900, 218152900

Offset

1,1

Comments

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

pows[max_] := Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]];
seq[max_] := Select[pows[max], eWeirdQ]; seq[5000] (* using the function "eWeirdQ" from A321146 *)

Crossrefs

Intersection of A001694 and A321146.

Cf. A005117, A391143.

Sequence in context: A321146 A391142 A374500 * A107545 A256363 A031568

Adjacent sequences: A391141 A391142 A391143 * A391145 A391146 A391147

Keyword

nonn

Author

Amiram Eldar, Dec 01 2025

Status

approved