A392009 Even squarefree integers with at least 3 prime factors.

30, 42, 66, 70, 78, 102, 110, 114, 130, 138, 154, 170, 174, 182, 186, 190, 210, 222, 230, 238, 246, 258, 266, 282, 286, 290, 310, 318, 322, 330, 354, 366, 370, 374, 390, 402, 406, 410, 418, 426, 430, 434, 438, 442, 462, 470, 474, 494, 498, 506, 510, 518, 530, 534

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Charles Kusniec, Composite Numbers Map for the OEIS.

Charles Kusniec, Distribution of gaps in A392009 for the first 5650 terms

Formula

a(n) = 2*A024556(n).

Example

The smallest even squarefree number with exactly 3 distinct prime factors is 30 = 2*3*5.

Mathematica

Select[Range[2, 534, 2], SquareFreeQ[#] && PrimeOmega[#] >= 3 &] (* Michael De Vlieger, Dec 29 2025 *)

Prog

(Python)
from math import isqrt
from sympy import primepi, mobius
from oeis_sequences.OEISsequences import bisection
def A392009(n):
    if n == 1: return 30
    def f(x): return int(n+x+primepi(y:=x>>1)-sum(mobius(k)*(y//k**2+1>>1) for k in range(1, isqrt(y)+1, 2)))
    return bisection(f, n, n) # Chai Wah Wu, Jan 07 2026

Crossrefs

The even elements of A350352.

Cf. A392008, A075819, A053858, A001221, A001222.

Sequence in context: A350352 A093599 A007304 * A160350 A053858 A075819

Adjacent sequences: A392006 A392007 A392008 * A392010 A392011 A392012

Keyword

nonn

Author

Charles Kusniec, Dec 26 2025

Status

approved