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A392008
Odd squarefree integers with at least 3 prime factors.
2
105, 165, 195, 231, 255, 273, 285, 345, 357, 385, 399, 429, 435, 455, 465, 483, 555, 561, 595, 609, 615, 627, 645, 651, 663, 665, 705, 715, 741, 759, 777, 795, 805, 861, 885, 897, 903, 915, 935, 957, 969, 987, 1001, 1005, 1015, 1023, 1045, 1065, 1085, 1095, 1105, 1113, 1131, 1155
OFFSET
1,1
EXAMPLE
The smallest odd squarefree number with exactly 3 distinct prime factors is 105 = 3*5*7.
MAPLE
q:= n-> (l-> nops(l)>2 and {l[]}={1})(ifactors(n)[2][.., 2]):
select(q, [2*i+1$i=0..577])[]; # Alois P. Heinz, Dec 29 2025
MATHEMATICA
Select[Range[1, 1160, 2], SquareFreeQ[#] && PrimeOmega[#] >= 3 &] (* Michael De Vlieger, Dec 29 2025 *)
PROG
(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
from oeis_sequences.OEISsequences import bisection
def A392008(n):
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b+1, isqrt(x//c)+1), a+1)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b+1, integer_nthroot(x//c, m)[0]+1), a+1) for d in g(x, a2, b2, c*b2, m-1)))
def f(x): return int(n+x-sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 1, 2, 1, i)) for i in range(3, x.bit_length())))
return bisection(f, n, n) # Chai Wah Wu, Jan 07 2026
CROSSREFS
The odd elements of A350352.
Superset of A046389.
Sequence in context: A013590 A216918 A278569 * A046389 A154430 A118678
KEYWORD
nonn
AUTHOR
Charles Kusniec, Dec 26 2025
STATUS
approved