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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A033950, A157932, A336041.

Sequence in context: A109807 A259645 A191113 * A125964 A288526 A139544

Adjacent sequences: A345208 A345209 A345210 * A345212 A345213 A345214

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 10 2021

Status

approved