A099611 a(n) is the largest odd number that is less than n^2 and is the product of two distinct primes.

15, 21, 35, 39, 57, 77, 95, 119, 143, 161, 187, 221, 253, 287, 323, 355, 395, 437, 481, 527, 573, 623, 671, 723, 781, 835, 899, 959, 1011, 1081, 1149, 1219, 1293, 1363, 1441, 1517, 1591, 1679, 1763, 1843, 1929, 2021, 2105, 2201, 2291, 2395, 2497, 2599, 2701

Offset

4,1

Comments

a(n) < A000290(n) < A099610(n); subsequence of A046388.

The offset is 4 since a(n) does not exist for n <= 3.

Links

Table of n, a(n) for n=4..52.

Mathematica

Module[{nn=70, p2p}, p2p=Reverse[Union[Times@@@Subsets[Prime[Range[ 2, PrimePi[ Ceiling[ nn^2/3]]]], {2}]]]; Table[SelectFirst[p2p, #<n^2&], {n, 4, nn}]] (* Harvey P. Dale, Dec 06 2021 *)

Prog

(Python)
from itertools import count
from sympy import factorint
def A099611(n):
    for i in count(n**2-(n%2)-1, -2):
        fs = factorint(i)
        if len(fs) == 2 == sum(fs.values()):
            return i # Chai Wah Wu, Dec 06 2021
(PARI) a(n) = forstep(k=n^2-n%2-1, 1, -2, if (bigomega(k)==2&&omega(k)==2, return(k))); \\ Michel Marcus, Dec 07 2021

Crossrefs

Cf. A000290, A006881, A099610, A349809.

Sequence in context: A309005 A225916 A128279 * A081934 A095147 A081977

Adjacent sequences: A099608 A099609 A099610 * A099612 A099613 A099614

Keyword

nonn

Author

Reinhard Zumkeller, Oct 25 2004

Extensions

Definition clarified by N. J. A. Sloane, Dec 06 2021

Status

approved