A099610 a(n) is the smallest odd number that is greater than n^2 and is the product of two distinct primes.

15, 15, 15, 21, 33, 39, 51, 65, 85, 111, 123, 145, 177, 201, 235, 259, 291, 327, 365, 403, 445, 485, 533, 579, 629, 679, 731, 785, 843, 901, 965, 1027, 1099, 1157, 1227, 1299, 1371, 1457, 1527, 1603, 1685, 1765, 1851, 1937, 2031, 2117, 2215, 2305, 2407, 2501, 2603, 2705, 2811, 2921, 3027, 3139, 3261, 3365, 3487, 3601, 3737, 3845, 3973, 4097, 4227, 4359, 4497, 4627

Offset

1,1

Comments

A099611(n) < A000290(n) < a(n); subsequence of A046388.

This is an "arithmetic" sequence (like sigma(n)), so it has offset 1. - N. J. A. Sloane, Dec 06 2021

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Maple

with(numtheory);
A099610 := proc(n) local M, i, t1, tt;
M:=100; t1:=n^2;
for i from 1 to M do
  tt:=t1+i;
  if (tt mod 2) = 1 and tau(tt) = 4 and nops(factorset(tt)) = 2 then return(tt); fi;
od:
lprint("error: the internal parameter M needs to be increased");
end proc; # N. J. A. Sloane, Dec 05 2021

Mathematica

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

Prog

(Python)
from itertools import count
from sympy import factorint
def A099610(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 05 2021

Crossrefs

Cf. A000290, A046388, A099611, A349806 (a(n)-n^2).

Sequence in context: A346623 A225917 A140806 * A085321 A239315 A003890

Adjacent sequences: A099607 A099608 A099609 * A099611 A099612 A099613

Keyword

nonn

Author

Reinhard Zumkeller, Oct 25 2004

Extensions

Edited and corrected by Harvey P. Dale and N. J. A. Sloane, Dec 05 2021

Status

approved