A391143 Primitive exponential pseudoperfect numbers: powerful numbers equal to the sum of a subset of their proper exponential divisors.

36, 900, 1764, 1800, 2700, 3600, 4356, 4500, 6084, 7056, 8100, 10404, 12348, 12996, 17424, 19044, 22500, 30276, 34596, 44100, 47916, 49284, 60516, 66564, 79092, 79524, 86436, 88200, 101124, 108900, 112500, 125316, 132300, 133956, 152100, 161604, 176400, 176868, 181476, 191844

Offset

1,1

Comments

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).

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

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], ePspQ]; seq[64000] (* using the function "ePspQ" from A318100 *)

Crossrefs

Intersection of A001694 and A318100.

Cf. A005117, A391144.

Sequence in context: A229680 A169836 A391087 * A391089 A335220 A248108

Adjacent sequences: A391140 A391141 A391142 * A391144 A391145 A391146

Keyword

nonn

Author

Amiram Eldar, Dec 01 2025

Status

approved