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%I #17 Nov 21 2018 13:45:58
%S 4,-14,-196,480,696,-57901,-525364,-409579,18528507,-237549252,
%T -2119519900,6713972874,18262155072,-19072020914992,162234208372185,
%U 1471912942112734,6828673030820538,-35126752028893500,729026655790306778,-15365360727898374618
%N Determinant of n X n matrix containing the first n^2 semiprimes in increasing order.
%C Semiprime analog of A067276 Determinant of n X n matrix containing the first n^2 primes in increasing order. The first column contains the first n semiprimes in increasing order, the second column contains the next n semiprimes in increasing order, etc. Equivalently, first row contains first n semiprimes in increasing order, second row contains next n semiprimes in increasing order, etc. See also: A118713 a(n) = determinant of n X n circulant matrix whose first row is A001358(1), A001358(2), ..., A001358(n) where A001358(n) = n-th semiprime.
%H Harvey P. Dale, <a href="/A118770/b118770.txt">Table of n, a(n) for n = 1..570</a>
%e a(2) = -14 because of the determinant -14 =
%e |4,6 |
%e |9,10|.
%e a(6) = -57901 = the determinant
%e |4, 6, 9, 10, 14, 15,|
%e |21, 22, 25, 26, 33, 34,|
%e |35, 38, 39, 46, 49, 51,|
%e |55, 57, 58, 62, 65, 69,|
%e |74, 77, 82, 85, 86, 87,|
%e |91, 93, 94, 95, 106, 111|.
%t SemiPrimePi[ n_ ] := Sum[ PrimePi[ n/Prime @ i ] - i + 1, {i, PrimePi @ Sqrt @ n} ]; SemiPrime[ n_ ] := Block[ {e = Floor[ Log[ 2, n ] + 1 ], a, b}, a = 2^e; Do[ b = 2^p; While[ SemiPrimePi[ a ] < n, a = a + b ]; a = a - b/2, {p, e, 0, -1} ]; a + b/2 ]; Table[ Det[ Partition[ Array[ SemiPrime, n^2 ], n ] ], {n, 20} ] (* _Robert G. Wilson v_, May 26 2006 *)
%t Module[{nn=5000,spr},spr=Select[Range[nn],PrimeOmega[#]==2&];Table[Det[ Partition[ Take[spr,n^2],n]],{n,Sqrt[Length[spr]]}]] (* _Harvey P. Dale_, Nov 21 2018 *)
%Y Cf. A001358, A067276, A118713, A118772, A118779.
%K easy,sign
%O 1,1
%A _Jonathan Vos Post_, May 22 2006
%E More terms from _Robert G. Wilson v_, May 26 2006
%E Typos in Mma program corrected by _Giovanni Resta_, Jun 12 2016
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