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Squarefree semiprimes of the form (2*p - 3) * (3*p - 2), p prime.
4

%I #6 Jul 20 2022 12:53:30

%S 21,91,209,589,851,2881,7739,10541,16171,26069,29329,75151,95129,

%T 110839,165169,194219,216409,220991,264389,374749,411601,653069,

%U 717949,829931,1108969,1119311,1171741,1269139,1416689,2059789,3161729,3374249,3428459,4924109

%N Squarefree semiprimes of the form (2*p - 3) * (3*p - 2), p prime.

%C a(n) = (2*A259730(n) - 3) * (3*A259730(n) - 2);

%C 3431 = A033569(24) = (2*25-3)*(3*25-2) = 47*73 = A006881(946) is the smallest term in the intersection of A006881 and A033569 not belonging to this sequence.

%H Reinhard Zumkeller, <a href="/A259758/b259758.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 6*A259730(n)^2 - 13*A259730(n) + 6.

%e . n | p = A259730(n) | 2*p - 3 | 3*p - 2 | a(n)

%e . ----+----------------+---------+---------+--------

%e . 1 | 3 | 3 | 7 | 21

%e . 2 | 5 | 7 | 13 | 91

%e . 3 | 7 | 11 | 19 | 209

%e . 4 | 11 | 19 | 31 | 589

%e . 5 | 13 | 23 | 37 | 851

%e . 6 | 23 | 43 | 67 | 2881

%e . 7 | 37 | 71 | 109 | 7739

%e . 8 | 43 | 83 | 127 | 10541

%e . 9 | 53 | 103 | 157 | 16171

%e . 10 | 67 | 131 | 199 | 26069

%e . 11 | 71 | 139 | 211 | 29329

%e . 12 | 113 | 223 | 337 | 75151 .

%t Select[Table[(2p-3)(3p-2),{p,Prime[Range[200]]}],PrimeOmega[#]==2&&SquareFreeQ[ #]&] (* _Harvey P. Dale_, Jul 20 2022 *)

%o (Haskell)

%o a259758 n = (2 * p - 3) * (3 * p - 2) where p = a259730 n

%Y Cf. A259730, subsequence of A006881, subsequence of A033569.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 05 2015