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A080508 Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose geometric mean is an integer. 5
1, 1, 4, 1, 2, 4, 1, 2, 3, 216, 1, 2, 3, 4, 324, 1, 2, 3, 4, 5, 6075000, 1, 2, 3, 4, 5, 6, 30375000, 1, 2, 3, 4, 5, 6, 7, 750453558750000, 1, 2, 3, 4, 5, 6, 7, 8, 19699405917187500, 1, 2, 3, 4, 5, 6, 7, 8, 9, 459652804734375000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9652708899421875000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The n-th row has the form {1,2,...,n-1,x}, where x is as small as possible.

LINKS

Robert Israel, Table of n, a(n) for n = 1..1485 (rows 1 to 54, flattened)

EXAMPLE

Triangle begins:

  1;

  1, 4;

  1, 2, 4;

  1, 2, 3, 216;

  1, 2, 3,   4, 324;

  1, 2, 3,   4,   5, 6075000;

  ...

MAPLE

f:= proc(n) local F;

  F:= ifactors((n-1)!)[2];

  mul(t[1]^(n-(t[2] mod n)), t=F)

end proc:

f(2):= 4:

seq(op([seq(j, j=1..i-1), f(i)]), i=1..20); # Robert Israel, Nov 04 2018

MATHEMATICA

MapAt[{First@ #, 4 Last@ #} &, Array[Append[Range[# - 1], Apply[Times, Prime@ Range@ PrimePi[# - 1]]^#/(# - 1)!] &, 11], 2] // Flatten (* Michael De Vlieger, Nov 05 2018 *)

CROSSREFS

Cf. A080509, A080510, A080504, A080511.

Sequence in context: A084454 A127812 A100353 * A178141 A063987 A236269

Adjacent sequences:  A080505 A080506 A080507 * A080509 A080510 A080511

KEYWORD

nonn,tabl

AUTHOR

Amarnath Murthy, Mar 20 2003

EXTENSIONS

More terms using A080509 from Michel Marcus, Nov 04 2018

STATUS

approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)