A067546 Determinant of an n X n matrix whose diagonal are the first n nonprime numbers and all other elements are 1's.

1, 3, 15, 105, 840, 7560, 83160, 1081080, 15135120, 227026800, 3859455600, 73329656400, 1466593128000, 30798455688000, 708364480824000, 17000747539776000, 425018688494400000, 11050485900854400000, 298363119323068800000, 8652530460368995200000, 268228444271438851200000

Offset

1,2

Links

Peter Luschny, Table of n, a(n) for n = 1..100

Example

The matrix begins:
1 1 1 1 1 1 1 ...
1 4 1 1 1 1 1 ...
1 1 6 1 1 1 1 ...
1 1 1 8 1 1 1 ...
1 1 1 1 9 1 1 ...
1 1 1 1 1 10 1 ...

Maple

A067546 := proc(n) local np, f, a; with(linalg);
np := proc(n) option remember; if n <= 1 then 1 else for a from np(n-1)+1 do
if not isprime(a) then return(a) fi od fi end:
f := (i, j) -> `if`(i=j, np(i), 1); det(matrix(n, n, f)) end:
seq(A067546(i), i=1..18);  # Peter Luschny, May 28 2013

Mathematica

NonPrime[ n_Integer ] := FixedPoint[ n + PrimePi[ # ] &, n + PrimePi[ n ] ]; Table[ Det[ DiagonalMatrix[ Table[ NonPrime[ i ] - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ]

Crossrefs

Sequence in context: A001801 A323551 A267840 * A015682 A291744 A246860

Adjacent sequences: A067543 A067544 A067545 * A067547 A067548 A067549

Keyword

nonn

Author

Robert G. Wilson v, Jan 28 2002

Status

approved