A392262 Even composite numbers that are squarefree or powers of 2.

4, 6, 8, 10, 14, 16, 22, 26, 30, 32, 34, 38, 42, 46, 58, 62, 64, 66, 70, 74, 78, 82, 86, 94, 102, 106, 110, 114, 118, 122, 128, 130, 134, 138, 142, 146, 154, 158, 166, 170, 174, 178, 182, 186, 190, 194, 202, 206, 210, 214, 218, 222, 226, 230, 238, 246, 254

Offset

1,1

Comments

Even composite numbers x whose prime factorization has either one power of 2 or distinct primes (necessarily including 2).

Even composite numbers x for which there exists y with 1 <= y <= floor(x/4) such that x*y is a square number (for powers of 2), or such that x*y is an oblong number (for even squarefree x).

Omega(x) = omega(x) >= 2 (for even squarefree composites), Omega(x) > omega(x) = 1 (for proper powers of 2).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Charles Kusniec, Composite Numbers Map for the OEIS.

Formula

Disjoint union of A000079 \ {1,2} and A039956 \ {2}.

Mathematica

Select[Range[4, 256, 2], SquareFreeQ[#] || DigitSum[#, 2] == 1 &] (* Paolo Xausa, Jan 12 2026 *)

Prog

(Python)
from math import isqrt
from sympy import mobius
from oeis_sequences.OEISsequences import bisection
def A392262(n):
    def f(x): return int(n+x+3-sum(mobius(k)*((x>>1)//k**2+1>>1) for k in range(1, isqrt(x>>1)+1, 2))-x.bit_length())
    return bisection(f, n, n) # Chai Wah Wu, Jan 26 2026

Crossrefs

Equals A388427 \ A390760.

Even terms of A388427.

Cf. A039956 \ {2} (even squarefree composites), A000079 \ {1, 2} (power of 2 composites), A001221, A001222.

Sequence in context: A383276 A395766 A392493 * A328144 A327888 A103800

Adjacent sequences: A392259 A392260 A392261 * A392263 A392264 A392265

Keyword

nonn

Author

Charles Kusniec, Jan 05 2026

Status

approved