A348097 Numbers having equally many unitary and nonunitary prime divisors.

1, 12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 63, 68, 75, 76, 80, 88, 92, 96, 98, 99, 104, 112, 116, 117, 124, 135, 136, 147, 148, 152, 153, 160, 162, 164, 171, 172, 175, 176, 184, 188, 189, 192, 207, 208, 212, 224, 232, 236, 242, 244, 245, 248, 250, 261

Offset: 1

Author

Amiram Eldar, Sep 30 2021

Keywords

• nonn

Comments

A prime divisor of k is unitary if its exponent in the prime factorization of k is 1, and is nonunitary otherwise.

Numbers k such that A056169(k) = A056170(k) = A001221(k)/2.

A345381 is a subsequence. After a(1) = 1, a(238) = 1260 is the next term that is not in A345381.

Examples

			12 = 2^2 * 3 is a term since it has one unitary prime divisor (3) and one nonunitary prime divisor (2).
		

Links

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

Crossrefs

Cf. A001221, A056169, A056170, A345381.

Subsequence of A030231.

Similar sequences: A016825 (odd and even divisors), A048109, A187039.

Programs

Mathematica

q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), 1] == Length[e]/2; Select[Range[300], q]