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A122964 Semiprimes with triangular indices. 1

%I #11 Apr 24 2018 14:41:12

%S 4,9,15,26,39,58,85,111,134,166,205,237,291,327,382,445,497,545,623,

%T 697,766,841,921,1003,1114,1195,1285,1379,1486,1622,1718,1837,1943,

%U 2071,2195,2329,2483,2605,2787,2935,3073,3214,3379,3554,3742,3909,4105,4286

%N Semiprimes with triangular indices.

%H Harvey P. Dale, <a href="/A122964/b122964.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = semiprime(T(1)), where T(n) is the n-th triangular number. a(n) = A001358(A000217(n)) = A001358(n*(n+1)/2).

%e a(1) = semiprime(T(1)) = semiprime(1) = 4 = 2^2.

%e a(2) = semiprime(T(2)) = semiprime(3) = 9 = 3^2.

%e a(3) = semiprime(T(3)) = semiprime(6) = 15 = 3 * 5.

%e a(4) = semiprime(T(4)) = semiprime(10) = 26 = 2 * 13.

%t Module[{nn=3000,sem,tr,len},sem=Select[Range[nn],PrimeOmega[#]==2&];len = Length[sem];tr=Table[If[OddQ[Sqrt[8n+1]],1,0],{n,len}];Pick[ sem,tr,1]](* _Harvey P. Dale_, Apr 24 2018 *)

%Y Cf. A000217, A001358.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Oct 27 2006

%E a(24)-a(48) from _Giovanni Resta_, Jun 13 2016

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