A348121 Numbers having more nonunitary than unitary prime divisors.

4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 180, 196, 200, 216, 225, 243, 252, 256, 288, 289, 300, 324, 343, 360, 361, 392, 396, 400, 432, 441, 450, 468, 484, 500, 504, 512, 529, 540, 576, 588, 600, 612, 625, 648, 675, 676, 684

Offset: 1

Author

Amiram Eldar, Oct 01 2021

Keywords

• nonn

Comments

First differs from A080366 at n = 20.

The first 19 terms are also the first 19 powerful numbers (A001694) above 1. a(20) = 180 is the least nonpowerful term.

Numbers k such that A056169(k) < A056170(k).

Examples

			4 = 2^2 is a term since it has 1 nonunitary prime divisor, 2, and no unitary prime divisors.
180 = 2^2 * 3^2 * 5 is a term since it has 2 nonunitary prime divisors, 2 and 3, and one unitary prime divisor, 5.
		

Links

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

Crossrefs

Cf. A056169, A056170, A348097.

Subsequence of A013929.

A001694 is a subsequence.

Programs

Mathematica

q[n_] := 2*Count[(e = FactorInteger[n][[;; , 2]]), 1] < Length[e]; Select[Range[700], q]