A118772 Determinant of n X n matrix containing the first n^2 3-almost primes in increasing order.

8, -56, 156, 13328, -920, -83678, 1261988, 54252742, 214409844, -3528354250, 247094703588, -509185323508, 15154985424718, 884710401396570, 49777180907707320, -172913218088289027, 844641410704177098, 3066058962037715903, -33948947842497666568

Offset

1,1

Comments

3-almost prime 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 3-almost primes in increasing order, the second column contains the next n 3-almost primes in increasing order, etc. Equivalently, first row contains first n 3-almost primes in increasing order, second row contains next n 3-almost primes in increasing order, etc. See also: A118713 a(n) = semiprime circulant.

Links

Table of n, a(n) for n=1..19.

Example

a(2) = -56 because of the determinant -56 =
|8, 12|
18, 20|.
a(6) = -83678 because of the determinant -83678 =
| 8, 12, 18, 20, 27, 28|
| 30, 42, 44, 45, 50, 52|
| 63, 66, 68, 70, 75, 76|
| 78, 92, 98, 99, 102, 105|
| 110, 114, 116, 117, 124, 125|
| 130, 138, 147, 148, 153, 154|.

Mathematica

ThreeAlmostPrimePi[ n_ ] := Sum[ PrimePi[ n/(Prime @ i*Prime @ j) ] - j + 1, {i, PrimePi[ n^(1/3) ]}, {j, i, PrimePi@ Sqrt[ n/Prime @ i ]} ]; ThreeAlmostPrime[ n_ ] := Block[ {e = Floor[ Log[ 2, n ] + 1 ], a, b}, a = 2^e; Do[ b = 2^p; While[ ThreeAlmostPrimePi[ a ] < n, a = a + b ]; a = a - b/2, {p, e, 0, -1} ]; a + b/2 ]; Table[ Det[ Partition[ Array[ ThreeAlmostPrime, n^2 ], n ] ], {n, 19} ] (* Robert G. Wilson v, May 26 2006 *)
With[{tap=Select[Range[4000], PrimeOmega[#]==3&]}, Table[Det[ Partition[ Take[tap, n^2], n]], {n, 20}]] (* Harvey P. Dale, Apr 17 2020 *)

Crossrefs

Cf. A014612, A067276, A118713, A118770, A118779.

Sequence in context: A003722 A364124 A044146 * A212817 A355948 A267522

Adjacent sequences: A118769 A118770 A118771 * A118773 A118774 A118775

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