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A118770 Determinant of n X n matrix containing the first n^2 semiprimes in increasing order. 5
4, -14, -196, 480, 696, -57901, -525364, -409579, 18528507, -237549252, -2119519900, 6713972874, 18262155072, -19072020914992, 162234208372185, 1471912942112734, 6828673030820538, -35126752028893500, 729026655790306778, -15365360727898374618 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..570

EXAMPLE

a(2) = -14 because of the determinant -14 =

|4,6 |

|9,10|.

a(6) = -57901 = the determinant

|4, 6, 9, 10, 14, 15,|

|21, 22, 25, 26, 33, 34,|

|35, 38, 39, 46, 49, 51,|

|55, 57, 58, 62, 65, 69,|

|74, 77, 82, 85, 86, 87,|

|91, 93, 94, 95, 106, 111|.

MATHEMATICA

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 *)

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 *)

CROSSREFS

Cf. A001358, A067276, A118713, A118772, A118779.

Sequence in context: A129225 A129226 A003010 * A226943 A292708 A112514

Adjacent sequences:  A118767 A118768 A118769 * A118771 A118772 A118773

KEYWORD

easy,sign

AUTHOR

Jonathan Vos Post, May 22 2006

EXTENSIONS

More terms from Robert G. Wilson v, May 26 2006

Typos in Mma program corrected by Giovanni Resta, Jun 12 2016

STATUS

approved

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Last modified July 12 06:46 EDT 2020. Contains 335658 sequences. (Running on oeis4.)