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

1,1

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).

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A056169, A056170, A348097.

Subsequence of A013929.

A001694 is a subsequence.

Sequence in context: A158804 A341645 A339497 * A080366 A001694 A377821

Adjacent sequences: A348118 A348119 A348120 * A348122 A348123 A348124

Keyword

nonn

Author

Amiram Eldar, Oct 01 2021

Status

approved