A071248
a(n) = Product_{k=1..n} lcm(n,k).
Original entry on oeis.org
1, 4, 54, 768, 75000, 466560, 592950960, 5284823040, 1735643790720, 45360000000000, 1035338990313196800, 102980960177356800, 145077660657859734604800, 154452450072526199193600
Offset: 1
Product of terms in n-th row of
A051173.
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A071248 := proc(n) mul( lcm(k,n),k=1..n) ; end: for n from 1 to 10 do printf("%d ",A071248(n)) ; od ; # R. J. Mathar, Apr 03 2007
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Table[Product[LCM[k,n],{k,n}],{n,20}] (* Harvey P. Dale, Jun 12 2019 *)
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a(n)=prod(k=1,n,lcm(n,k))
A203904
Triangular array T; for n>0, row n shows the coefficients of a reduced polynomial having zeros -k/(n+1) for k=1,2,...,n.
Original entry on oeis.org
1, 1, 2, 2, 9, 9, 3, 22, 48, 32, 24, 250, 875, 1250, 625, 10, 137, 675, 1530, 1620, 648, 720, 12348, 79576, 252105, 420175, 352947, 117649, 315, 6534, 52528, 216608, 501760, 659456, 458752, 131072, 4480, 109584, 1063116, 5450004, 16365321
Offset: 1
First five rows(counting the top row as row 0):
1
1...2.................representing 1+2x
1...9...9.............representing 2+9x+9x^2
3...22..48...32
24...250...875...1250...625
Zeros corresponding to rows 1 to 4:
.................-1/2
............-2/3......-1/3
......-3/4.......-1/2.......-1/4
-4/5........-3/5......-2/5.......-1/5
Interlace property for successive rows illustrated by
1/5 < 1/4 < 2/5 < 1/2 < 3/5 < 3/4 < 4/5.
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p[n_, x_] := Product[(n*x + k)/GCD[n, k], {k, 1, n - 1}]
Table[CoefficientList[p[n, x], x], {n, 1, 10}]
TableForm[%] (* A203904 triangle *)
Flatten[%%] (* A203904 sequence *)
A308944
a(n) = Product_{k=1..n} lcm(n,k) / (k * gcd(n,k)).
Original entry on oeis.org
1, 1, 3, 4, 125, 9, 16807, 1024, 59049, 15625, 2357947691, 5184, 1792160394037, 282475249, 474609375, 17179869184, 2862423051509815793, 3486784401, 5480386857784802185939, 250000000000, 10382917022245341, 5559917313492231481, 39471584120695485887249589623
Offset: 1
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Table[Product[LCM[n, k]/(k GCD[n, k]), {k, 1, n}], {n, 1, 23}]
Table[Product[d^(EulerPhi[d] - EulerPhi[n/d]), {d, Divisors[n]}], {n, 1, 23}]
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a(n) = prod(k=1, n, lcm(n, k)/(k*gcd(n, k))); \\ Michel Marcus, Jul 02 2019
Showing 1-3 of 3 results.
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