A135873 Multiply the positive integers which are coprime to n in order (starting at 1). a(n) is the largest such partial product that is <= n.

1, 1, 2, 3, 2, 5, 6, 3, 8, 3, 6, 5, 6, 3, 8, 15, 6, 5, 6, 3, 8, 15, 6, 5, 24, 15, 8, 15, 24, 7, 24, 15, 8, 15, 24, 35, 24, 15, 8, 21, 24, 5, 24, 15, 8, 15, 24, 35, 24, 21, 40, 15, 24, 35, 24, 15, 40, 15, 24, 7, 24, 15, 40, 15, 24, 35, 24, 15, 40, 27, 24, 35, 24, 15, 56, 15, 24, 35, 24

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The positive integers which are coprime to 9 begin: 1,2,4,5,7,8,10,11,... Checking the partial products: 1=1, 1*2=2, 1*2*4 = 8, 1*2*4*5 =40,... 8 is the largest such partial product which is <= 9. So a(9) = 8.

Mathematica

a = {}; For[n = 1, n < 80, n++, p = 1; i = 1; While[p < n, i++; If[GCD[i, n] == 1, p = p*i]]; AppendTo[a, p/i]]; a (* Stefan Steinerberger, Feb 06 2008 *)
Table[SelectFirst[Reverse[FoldList[Times, Select[Range[n], CoprimeQ[#, n]&]]], #<=n&], {n, 80}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 02 2018 *)

Crossrefs

Cf. A135872.

Sequence in context: A276270 A349668 A214571 * A070673 A070669 A218613

Adjacent sequences: A135870 A135871 A135872 * A135874 A135875 A135876

Keyword

nonn

Author

Leroy Quet, Dec 03 2007

Extensions

More terms from Stefan Steinerberger, Feb 06 2008

Status

approved