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11-gonal (or hendecagonal) numbers which are products of two distinct primes.
0

%I #14 May 31 2022 15:38:16

%S 58,95,141,415,1241,2101,2951,3683,6031,7421,16531,24383,35333,39433,

%T 42001,50191,53083,66551,83981,95411,123421,146791,173951,182911,

%U 190241,229051,296321,307981,336883,409361,442583,451091,477101,500833,546883,588431,669131

%N 11-gonal (or hendecagonal) numbers which are products of two distinct primes.

%C A squarefree subsequence of 11-gonal numbers, i.e., numbers of the form k*(9*k-7)/2.

%e 58 = 4*(9*4 - 7)/2 = 2*29;

%e 141 = 6*(9*6 - 7)/2 = 3*47;

%e 415 = 10*(9*10 - 7)/2 = 5*83;

%e 3683 = 29*(9*29 - 7)/2 = 29*127.

%t Select[Table[n*(9*n - 7)/2, {n, 1, 400}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* _Amiram Eldar_, May 30 2022 *)

%o (Python)

%o from sympy import factorint

%o from itertools import count, islice

%o def agen():

%o for h in (k*(9*k - 7)//2 for k in count(1)):

%o f = factorint(h, multiple=True)

%o if len(f) == len(set(f)) == 2: yield h

%o print(list(islice(agen(), 37))) # _Michael S. Branicky_, May 30 2022

%Y Intersection of A051682 and A006881.

%K nonn

%O 1,1

%A _Massimo Kofler_, May 30 2022