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A354448
11-gonal (or hendecagonal) numbers which are products of two distinct primes.
0
58, 95, 141, 415, 1241, 2101, 2951, 3683, 6031, 7421, 16531, 24383, 35333, 39433, 42001, 50191, 53083, 66551, 83981, 95411, 123421, 146791, 173951, 182911, 190241, 229051, 296321, 307981, 336883, 409361, 442583, 451091, 477101, 500833, 546883, 588431, 669131
OFFSET
1,1
COMMENTS
A squarefree subsequence of 11-gonal numbers, i.e., numbers of the form k*(9*k-7)/2.
EXAMPLE
58 = 4*(9*4 - 7)/2 = 2*29;
141 = 6*(9*6 - 7)/2 = 3*47;
415 = 10*(9*10 - 7)/2 = 5*83;
3683 = 29*(9*29 - 7)/2 = 29*127.
MATHEMATICA
Select[Table[n*(9*n - 7)/2, {n, 1, 400}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* Amiram Eldar, May 30 2022 *)
PROG
(Python)
from sympy import factorint
from itertools import count, islice
def agen():
for h in (k*(9*k - 7)//2 for k in count(1)):
f = factorint(h, multiple=True)
if len(f) == len(set(f)) == 2: yield h
print(list(islice(agen(), 37))) # Michael S. Branicky, May 30 2022
CROSSREFS
Intersection of A051682 and A006881.
Sequence in context: A044033 A266451 A124680 * A181462 A260603 A188238
KEYWORD
nonn
AUTHOR
Massimo Kofler, May 30 2022
STATUS
approved