A345211 Numbers with the same number of odd / even, refactorable divisors.

2, 4, 6, 10, 14, 18, 20, 22, 26, 28, 30, 34, 38, 42, 44, 46, 50, 52, 54, 58, 62, 66, 68, 70, 74, 76, 78, 82, 86, 90, 92, 94, 98, 100, 102, 106, 110, 114, 116, 118, 122, 124, 126, 130, 134, 138, 140, 142, 146, 148, 150, 154, 158, 162, 164, 166, 170, 172, 174, 178, 182, 186, 188

Offset: 1

Author

Wesley Ivan Hurt, Jun 10 2021

Keywords

• nonn

Comments

All the terms are even. Conjecture: The sequence a(n)/2 is the complement of A157932 (verified for a(n) < 4*10^7). - Amiram Eldar, Oct 11 2023

Examples

			18 is in the sequence since it has 2 odd and 2 even, refactorable divisors: 1, 2, 9, and 18.
		

Links

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

Crossrefs

Cf. A033950, A157932, A336041.

Programs

Mathematica

q[n_] := DivisorSum[n, (-1)^# &, Divisible[#, DivisorSigma[0, #]] &] == 0; Select[Range[2, 200, 2], q] (* Amiram Eldar, Oct 11 2023 *)

PARI

is(n) = (n%2)! && sumdiv(n, d, (-1)^d * !(d % numdiv(d))) == 0; \\ Amiram Eldar, Oct 11 2023