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A099610 a(n) is the smallest odd number that is greater than n^2 and is the product of two distinct primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)