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A085542 Determinant of the n X n matrix M_(i,j)=i/gcd(i,j)=lcm(i,j)/j. 2
1, -1, 2, -2, 8, 16, -96, 96, -192, -768, 7680, 15360, -184320, -1105920, -8847360, 8847360, -141557760, -283115520, 5096079360, 20384317440, 244611809280, 2446118092800, -53814598041600, -107629196083200, 430516784332800, 5166201411993600, -10332402823987200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Determinant of a symmetric polynomial evaluated at x = 1 that starts:

{

{1,      1,      1,      1,      1},

{1, -1 + x,      1, -1 + x,      1},

{1,      1, -2 + x,      1,      1},

{1, -1 + x,      1,     -1,      1},

{1,      1,      1,      1, -4 + x}

} - Mats Granvik, Jul 22 2012

LINKS

Table of n, a(n) for n=1..27.

FORMULA

a(n+1)/a(n)= A023900(n+1) the reciprocity balance of n+1

a(n) = Prod(i=1..A000720(n), (1-A000040(i))^floor(n/A000040(i))). - Enrique Pérez Herrero, Jul 12 2012

MATHEMATICA

Clear[nn, t, n, k, M, x]; nnn = 27; a = Range[nnn]*0; Do[nn = ii; t[n_, 1] = 1; t[1, k_] = 1; t[n_, k_] := t[n, k] = If[n < k, If[And[n > 1, k > 1], x - Sum[t[k - i, n], {i, 1, n - 1}], 0], If[And[n > 1, k > 1], x - Sum[t[n - i, k], {i, 1, k - 1}], 0]];  x = 1;  M = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];  a[[ii]] = Det[M], {ii, 1, nnn}]; a (* Mats Granvik, Jul 22 2012 *)

PROG

(PARI) a(n)=matdet(matrix(n, n, i, j, i/gcd(i, j)))

CROSSREFS

Sequence in context: A016120 A188115 * A239682 A009725 A053098 A194588

Adjacent sequences:  A085539 A085540 A085541 * A085543 A085544 A085545

KEYWORD

sign

AUTHOR

Benoit Cloitre, Aug 19 2003

STATUS

approved

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Last modified October 23 21:35 EDT 2018. Contains 316541 sequences. (Running on oeis4.)